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









          $endgroup$













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            2 Answers
            2






            active

            oldest

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            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






























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