Isn't Combination just selection?












0












$begingroup$


So,
There is this question which I came across.
"Total no of handshakes among 15 people."
The answer seems to be just 15C2.
Isn't that just a way of selecting and not the number of handshakes?
I'm in grade 10th. So don't judge.






combinations







share|cite|improve this question











$endgroup$

















    0












    $begingroup$


    So,
    There is this question which I came across.
    "Total no of handshakes among 15 people."
    The answer seems to be just 15C2.
    Isn't that just a way of selecting and not the number of handshakes?
    I'm in grade 10th. So don't judge.






    combinations







    share|cite|improve this question











    $endgroup$















      0












      0








      0





      $begingroup$


      So,
      There is this question which I came across.
      "Total no of handshakes among 15 people."
      The answer seems to be just 15C2.
      Isn't that just a way of selecting and not the number of handshakes?
      I'm in grade 10th. So don't judge.






      combinations







      share|cite|improve this question











      $endgroup$




      So,
      There is this question which I came across.
      "Total no of handshakes among 15 people."
      The answer seems to be just 15C2.
      Isn't that just a way of selecting and not the number of handshakes?
      I'm in grade 10th. So don't judge.






      combinations




      combinations






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Dec 16 '18 at 8:34









      Eevee Trainer

      5,9761936




      5,9761936










      asked Dec 16 '18 at 8:26









      Jaimeblt1Jaimeblt1

      82




      82






















          2 Answers
          2






          active

          oldest

          votes


















          0












          $begingroup$

          I mean, $_{15}C_2$ gives a numerical result as well even if describes a method of selection:



          $$_{15}C_2 = frac{15!}{2! cdot (15-2)!}$$



          and generally



          $$_{n}C_r = frac{n!}{r! cdot (n-r)!}$$



          Do the calculations and boom, a number. $_{n}C_r$ is just a notation representing the underlying number (or, rather, the calculations leading up to that number), because who wants to write that fraction every single time?






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            I'm not quite sure. 15C2 in literal terms means, you select 2 objects out of 15. Nowhere does it say that selection is equal to the number of handshakes. Pardon if i'm missing something obvious.
            $endgroup$
            – Jaimeblt1
            Dec 16 '18 at 8:33












          • $begingroup$
            What are you unsure about?
            $endgroup$
            – Eevee Trainer
            Dec 16 '18 at 8:34










          • $begingroup$
            Check it out. I edited it.
            $endgroup$
            – Jaimeblt1
            Dec 16 '18 at 8:39










          • $begingroup$
            No, $_{15}C_2$ represents the number of ways in which you can choose $2$ objects from $15$. It does not mean "choose a single pair of $2$ from $15$" - it means the number of ways in whichiyou can choose those pairs. I guess, yes, you could argue that in the sense of languages and the usual connotation in English it means to choose $2$ from $15$, but if you go on to study math one day in more depth you'll realize that the mathematical meaning and the common/everyday meaning may differ greatly.
            $endgroup$
            – Eevee Trainer
            Dec 16 '18 at 8:43












          • $begingroup$
            Mathematicians make very poor poets, so to speak, and can suck at developing intuitive, not-confusing notations/conventions for various things. But either way, that's just how mathematical notation and standards have developed.
            $endgroup$
            – Eevee Trainer
            Dec 16 '18 at 8:43



















          1












          $begingroup$

          $_{15}C_2$ is the number of ways to select 2 people from 15 people (when order doesn't matter). This is exactly the number of handshakes that occur if $15$ people all shake hands with each other. There is one handshake for each set of 2 people.






          share|cite|improve this answer









          $endgroup$













            Your Answer





            StackExchange.ifUsing("editor", function () {
            return StackExchange.using("mathjaxEditing", function () {
            StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
            StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
            });
            });
            }, "mathjax-editing");

            StackExchange.ready(function() {
            var channelOptions = {
            tags: "".split(" "),
            id: "69"
            };
            initTagRenderer("".split(" "), "".split(" "), channelOptions);

            StackExchange.using("externalEditor", function() {
            // Have to fire editor after snippets, if snippets enabled
            if (StackExchange.settings.snippets.snippetsEnabled) {
            StackExchange.using("snippets", function() {
            createEditor();
            });
            }
            else {
            createEditor();
            }
            });

            function createEditor() {
            StackExchange.prepareEditor({
            heartbeatType: 'answer',
            autoActivateHeartbeat: false,
            convertImagesToLinks: true,
            noModals: true,
            showLowRepImageUploadWarning: true,
            reputationToPostImages: 10,
            bindNavPrevention: true,
            postfix: "",
            imageUploader: {
            brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
            contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
            allowUrls: true
            },
            noCode: true, onDemand: true,
            discardSelector: ".discard-answer"
            ,immediatelyShowMarkdownHelp:true
            });


            }
            });














            draft saved

            draft discarded


















            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3042367%2fisnt-combination-just-selection%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown

























            2 Answers
            2






            active

            oldest

            votes








            2 Answers
            2






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            0












            $begingroup$

            I mean, $_{15}C_2$ gives a numerical result as well even if describes a method of selection:



            $$_{15}C_2 = frac{15!}{2! cdot (15-2)!}$$



            and generally



            $$_{n}C_r = frac{n!}{r! cdot (n-r)!}$$



            Do the calculations and boom, a number. $_{n}C_r$ is just a notation representing the underlying number (or, rather, the calculations leading up to that number), because who wants to write that fraction every single time?






            share|cite|improve this answer









            $endgroup$













            • $begingroup$
              I'm not quite sure. 15C2 in literal terms means, you select 2 objects out of 15. Nowhere does it say that selection is equal to the number of handshakes. Pardon if i'm missing something obvious.
              $endgroup$
              – Jaimeblt1
              Dec 16 '18 at 8:33












            • $begingroup$
              What are you unsure about?
              $endgroup$
              – Eevee Trainer
              Dec 16 '18 at 8:34










            • $begingroup$
              Check it out. I edited it.
              $endgroup$
              – Jaimeblt1
              Dec 16 '18 at 8:39










            • $begingroup$
              No, $_{15}C_2$ represents the number of ways in which you can choose $2$ objects from $15$. It does not mean "choose a single pair of $2$ from $15$" - it means the number of ways in whichiyou can choose those pairs. I guess, yes, you could argue that in the sense of languages and the usual connotation in English it means to choose $2$ from $15$, but if you go on to study math one day in more depth you'll realize that the mathematical meaning and the common/everyday meaning may differ greatly.
              $endgroup$
              – Eevee Trainer
              Dec 16 '18 at 8:43












            • $begingroup$
              Mathematicians make very poor poets, so to speak, and can suck at developing intuitive, not-confusing notations/conventions for various things. But either way, that's just how mathematical notation and standards have developed.
              $endgroup$
              – Eevee Trainer
              Dec 16 '18 at 8:43
















            0












            $begingroup$

            I mean, $_{15}C_2$ gives a numerical result as well even if describes a method of selection:



            $$_{15}C_2 = frac{15!}{2! cdot (15-2)!}$$



            and generally



            $$_{n}C_r = frac{n!}{r! cdot (n-r)!}$$



            Do the calculations and boom, a number. $_{n}C_r$ is just a notation representing the underlying number (or, rather, the calculations leading up to that number), because who wants to write that fraction every single time?






            share|cite|improve this answer









            $endgroup$













            • $begingroup$
              I'm not quite sure. 15C2 in literal terms means, you select 2 objects out of 15. Nowhere does it say that selection is equal to the number of handshakes. Pardon if i'm missing something obvious.
              $endgroup$
              – Jaimeblt1
              Dec 16 '18 at 8:33












            • $begingroup$
              What are you unsure about?
              $endgroup$
              – Eevee Trainer
              Dec 16 '18 at 8:34










            • $begingroup$
              Check it out. I edited it.
              $endgroup$
              – Jaimeblt1
              Dec 16 '18 at 8:39










            • $begingroup$
              No, $_{15}C_2$ represents the number of ways in which you can choose $2$ objects from $15$. It does not mean "choose a single pair of $2$ from $15$" - it means the number of ways in whichiyou can choose those pairs. I guess, yes, you could argue that in the sense of languages and the usual connotation in English it means to choose $2$ from $15$, but if you go on to study math one day in more depth you'll realize that the mathematical meaning and the common/everyday meaning may differ greatly.
              $endgroup$
              – Eevee Trainer
              Dec 16 '18 at 8:43












            • $begingroup$
              Mathematicians make very poor poets, so to speak, and can suck at developing intuitive, not-confusing notations/conventions for various things. But either way, that's just how mathematical notation and standards have developed.
              $endgroup$
              – Eevee Trainer
              Dec 16 '18 at 8:43














            0












            0








            0





            $begingroup$

            I mean, $_{15}C_2$ gives a numerical result as well even if describes a method of selection:



            $$_{15}C_2 = frac{15!}{2! cdot (15-2)!}$$



            and generally



            $$_{n}C_r = frac{n!}{r! cdot (n-r)!}$$



            Do the calculations and boom, a number. $_{n}C_r$ is just a notation representing the underlying number (or, rather, the calculations leading up to that number), because who wants to write that fraction every single time?






            share|cite|improve this answer









            $endgroup$



            I mean, $_{15}C_2$ gives a numerical result as well even if describes a method of selection:



            $$_{15}C_2 = frac{15!}{2! cdot (15-2)!}$$



            and generally



            $$_{n}C_r = frac{n!}{r! cdot (n-r)!}$$



            Do the calculations and boom, a number. $_{n}C_r$ is just a notation representing the underlying number (or, rather, the calculations leading up to that number), because who wants to write that fraction every single time?







            share|cite|improve this answer












            share|cite|improve this answer



            share|cite|improve this answer










            answered Dec 16 '18 at 8:29









            Eevee TrainerEevee Trainer

            5,9761936




            5,9761936












            • $begingroup$
              I'm not quite sure. 15C2 in literal terms means, you select 2 objects out of 15. Nowhere does it say that selection is equal to the number of handshakes. Pardon if i'm missing something obvious.
              $endgroup$
              – Jaimeblt1
              Dec 16 '18 at 8:33












            • $begingroup$
              What are you unsure about?
              $endgroup$
              – Eevee Trainer
              Dec 16 '18 at 8:34










            • $begingroup$
              Check it out. I edited it.
              $endgroup$
              – Jaimeblt1
              Dec 16 '18 at 8:39










            • $begingroup$
              No, $_{15}C_2$ represents the number of ways in which you can choose $2$ objects from $15$. It does not mean "choose a single pair of $2$ from $15$" - it means the number of ways in whichiyou can choose those pairs. I guess, yes, you could argue that in the sense of languages and the usual connotation in English it means to choose $2$ from $15$, but if you go on to study math one day in more depth you'll realize that the mathematical meaning and the common/everyday meaning may differ greatly.
              $endgroup$
              – Eevee Trainer
              Dec 16 '18 at 8:43












            • $begingroup$
              Mathematicians make very poor poets, so to speak, and can suck at developing intuitive, not-confusing notations/conventions for various things. But either way, that's just how mathematical notation and standards have developed.
              $endgroup$
              – Eevee Trainer
              Dec 16 '18 at 8:43


















            • $begingroup$
              I'm not quite sure. 15C2 in literal terms means, you select 2 objects out of 15. Nowhere does it say that selection is equal to the number of handshakes. Pardon if i'm missing something obvious.
              $endgroup$
              – Jaimeblt1
              Dec 16 '18 at 8:33












            • $begingroup$
              What are you unsure about?
              $endgroup$
              – Eevee Trainer
              Dec 16 '18 at 8:34










            • $begingroup$
              Check it out. I edited it.
              $endgroup$
              – Jaimeblt1
              Dec 16 '18 at 8:39










            • $begingroup$
              No, $_{15}C_2$ represents the number of ways in which you can choose $2$ objects from $15$. It does not mean "choose a single pair of $2$ from $15$" - it means the number of ways in whichiyou can choose those pairs. I guess, yes, you could argue that in the sense of languages and the usual connotation in English it means to choose $2$ from $15$, but if you go on to study math one day in more depth you'll realize that the mathematical meaning and the common/everyday meaning may differ greatly.
              $endgroup$
              – Eevee Trainer
              Dec 16 '18 at 8:43












            • $begingroup$
              Mathematicians make very poor poets, so to speak, and can suck at developing intuitive, not-confusing notations/conventions for various things. But either way, that's just how mathematical notation and standards have developed.
              $endgroup$
              – Eevee Trainer
              Dec 16 '18 at 8:43
















            $begingroup$
            I'm not quite sure. 15C2 in literal terms means, you select 2 objects out of 15. Nowhere does it say that selection is equal to the number of handshakes. Pardon if i'm missing something obvious.
            $endgroup$
            – Jaimeblt1
            Dec 16 '18 at 8:33






            $begingroup$
            I'm not quite sure. 15C2 in literal terms means, you select 2 objects out of 15. Nowhere does it say that selection is equal to the number of handshakes. Pardon if i'm missing something obvious.
            $endgroup$
            – Jaimeblt1
            Dec 16 '18 at 8:33














            $begingroup$
            What are you unsure about?
            $endgroup$
            – Eevee Trainer
            Dec 16 '18 at 8:34




            $begingroup$
            What are you unsure about?
            $endgroup$
            – Eevee Trainer
            Dec 16 '18 at 8:34












            $begingroup$
            Check it out. I edited it.
            $endgroup$
            – Jaimeblt1
            Dec 16 '18 at 8:39




            $begingroup$
            Check it out. I edited it.
            $endgroup$
            – Jaimeblt1
            Dec 16 '18 at 8:39












            $begingroup$
            No, $_{15}C_2$ represents the number of ways in which you can choose $2$ objects from $15$. It does not mean "choose a single pair of $2$ from $15$" - it means the number of ways in whichiyou can choose those pairs. I guess, yes, you could argue that in the sense of languages and the usual connotation in English it means to choose $2$ from $15$, but if you go on to study math one day in more depth you'll realize that the mathematical meaning and the common/everyday meaning may differ greatly.
            $endgroup$
            – Eevee Trainer
            Dec 16 '18 at 8:43






            $begingroup$
            No, $_{15}C_2$ represents the number of ways in which you can choose $2$ objects from $15$. It does not mean "choose a single pair of $2$ from $15$" - it means the number of ways in whichiyou can choose those pairs. I guess, yes, you could argue that in the sense of languages and the usual connotation in English it means to choose $2$ from $15$, but if you go on to study math one day in more depth you'll realize that the mathematical meaning and the common/everyday meaning may differ greatly.
            $endgroup$
            – Eevee Trainer
            Dec 16 '18 at 8:43














            $begingroup$
            Mathematicians make very poor poets, so to speak, and can suck at developing intuitive, not-confusing notations/conventions for various things. But either way, that's just how mathematical notation and standards have developed.
            $endgroup$
            – Eevee Trainer
            Dec 16 '18 at 8:43




            $begingroup$
            Mathematicians make very poor poets, so to speak, and can suck at developing intuitive, not-confusing notations/conventions for various things. But either way, that's just how mathematical notation and standards have developed.
            $endgroup$
            – Eevee Trainer
            Dec 16 '18 at 8:43











            1












            $begingroup$

            $_{15}C_2$ is the number of ways to select 2 people from 15 people (when order doesn't matter). This is exactly the number of handshakes that occur if $15$ people all shake hands with each other. There is one handshake for each set of 2 people.






            share|cite|improve this answer









            $endgroup$


















              1












              $begingroup$

              $_{15}C_2$ is the number of ways to select 2 people from 15 people (when order doesn't matter). This is exactly the number of handshakes that occur if $15$ people all shake hands with each other. There is one handshake for each set of 2 people.






              share|cite|improve this answer









              $endgroup$
















                1












                1








                1





                $begingroup$

                $_{15}C_2$ is the number of ways to select 2 people from 15 people (when order doesn't matter). This is exactly the number of handshakes that occur if $15$ people all shake hands with each other. There is one handshake for each set of 2 people.






                share|cite|improve this answer









                $endgroup$



                $_{15}C_2$ is the number of ways to select 2 people from 15 people (when order doesn't matter). This is exactly the number of handshakes that occur if $15$ people all shake hands with each other. There is one handshake for each set of 2 people.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Dec 16 '18 at 8:35









                littleOlittleO

                29.8k646109




                29.8k646109






























                    draft saved

                    draft discarded




















































                    Thanks for contributing an answer to Mathematics Stack Exchange!


                    • Please be sure to answer the question. Provide details and share your research!

                    But avoid …



                    • Asking for help, clarification, or responding to other answers.

                    • Making statements based on opinion; back them up with references or personal experience.


                    Use MathJax to format equations. MathJax reference.


                    To learn more, see our tips on writing great answers.




                    draft saved


                    draft discarded














                    StackExchange.ready(
                    function () {
                    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3042367%2fisnt-combination-just-selection%23new-answer', 'question_page');
                    }
                    );

                    Post as a guest















                    Required, but never shown





















































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown

































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown







                    -

                    Popular posts from this blog

                    Ellipse (mathématiques)

                    Image
                    Pour les articles homonymes, voir Ellipse. L'ellipse est le lieu des points dont la somme des distances à deux points fixes, dits foyers, est constante. Section du cône ou projection du cercle. En géométrie, une ellipse est une courbe plane fermée obtenue par l’intersection d’un cône de révolution avec un plan, à condition que celui-ci coupe l'axe de rotation du cône ou du cylindre : c'est une conique d'excentricité strictement comprise entre 0 et 1. On peut également la définir comme le lieu des points dont la somme des distances à deux points fixes, dits foyers, est constante (sa construction par la méthode du jardinier est très simple). Dans la vie courante, l’ellipse est la forme qu'on perçoit en regardant un cercle en perspective, ou la figure formée par l’ombre d'un disque sur une surface plane. On retrouve aussi, en première approximation [ 1 ] , des ellipses dans les trajectoires des corps célestes (planètes, comètes ou satellites arti...
                    Read more

                    Quarter-circle Tiles

                    Image
                    up vote 0 down vote favorite I have $99$ identical square tiles, each with a quarter-circle drawn on it like this: [asy] size(1.5cm); draw(Arc((2,0),1,90,180),red+1); draw((0,0)--(2,0)--(2,2)--(0,2)--(0,0)); [/asy] When I arrange the tiles in a $9times 11$ rectangular grid, each with a random orientation, what is the expected value of the number of full circles I form? I think this problem has to do with finding the chance any given 2x2 square has a circle, but I can't find it. expected-value share | cite | improve this question asked Nov 20 at 15:03 6minecraftninja 1 2 ...
                    Read more

                    Mont Emei

                    Image
                    Mont Emei.mw-parser-output .entete.map{background-image:url("//upload.wikimedia.org/wikipedia/commons/7/7a/Picto_infobox_map.png")} Vue du sommet Wanfo du mont Emei Géographie Altitude 3 099  m , Wanfo Coordonnées 29° 31′ 11″ nord, 103° 19′ 57″ est Administration Pays   Chine Province Sichuan Ville-préfecture Leshan Géolocalisation sur la carte : Sichuan Mont Emei Géolocalisation sur la carte : Chine Mont Emei modifier   Paysage panoramique du mont Emei, incluant le paysage panoramique du grand Bouddha de Leshan *   Patrimoine mondial de l'UNESCO Passerelle en bois sur le versant ouest Pays   Chine Subdivision Sichuan Type Mixte Critères (iv) (vi) (x) Superficie 15 400 ha Numéro d’identification 779 Zone géographique Asie et Pacifique  ** Année d’inscription 1996 (20 e session) * Descriptif officiel UNESCO ** Classification géog...
                    Read more