How many subsets of size 4 are there?












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All I can think of is there are $2^8$ subsets of the set. Then, there are $2^5$ subsets of size $5.$ So $2^8-2^5$ gives you the number of subsets of four elements. How do I even approach this problem?






combinatorics discrete-mathematics







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  • 4




    $begingroup$
    There aren't $2^5$ subsets of size $5$...there are $binom 85$. And why would the number of subsets of size $5$ plus the number of size $4$ equal the total number of subsets?
    $endgroup$
    – lulu
    Dec 14 '18 at 17:06


















0












$begingroup$


enter image description here



All I can think of is there are $2^8$ subsets of the set. Then, there are $2^5$ subsets of size $5.$ So $2^8-2^5$ gives you the number of subsets of four elements. How do I even approach this problem?






combinatorics discrete-mathematics







share|cite|improve this question











$endgroup$








  • 4




    $begingroup$
    There aren't $2^5$ subsets of size $5$...there are $binom 85$. And why would the number of subsets of size $5$ plus the number of size $4$ equal the total number of subsets?
    $endgroup$
    – lulu
    Dec 14 '18 at 17:06
















0












0








0





$begingroup$


enter image description here



All I can think of is there are $2^8$ subsets of the set. Then, there are $2^5$ subsets of size $5.$ So $2^8-2^5$ gives you the number of subsets of four elements. How do I even approach this problem?






combinatorics discrete-mathematics







share|cite|improve this question











$endgroup$




enter image description here



All I can think of is there are $2^8$ subsets of the set. Then, there are $2^5$ subsets of size $5.$ So $2^8-2^5$ gives you the number of subsets of four elements. How do I even approach this problem?






combinatorics discrete-mathematics




combinatorics discrete-mathematics






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 14 '18 at 17:07









user376343

3,7783827




3,7783827










asked Dec 14 '18 at 17:05









PumpkinpeachPumpkinpeach

628




628








  • 4




    $begingroup$
    There aren't $2^5$ subsets of size $5$...there are $binom 85$. And why would the number of subsets of size $5$ plus the number of size $4$ equal the total number of subsets?
    $endgroup$
    – lulu
    Dec 14 '18 at 17:06
















  • 4




    $begingroup$
    There aren't $2^5$ subsets of size $5$...there are $binom 85$. And why would the number of subsets of size $5$ plus the number of size $4$ equal the total number of subsets?
    $endgroup$
    – lulu
    Dec 14 '18 at 17:06










4




4




$begingroup$
There aren't $2^5$ subsets of size $5$...there are $binom 85$. And why would the number of subsets of size $5$ plus the number of size $4$ equal the total number of subsets?
$endgroup$
– lulu
Dec 14 '18 at 17:06






$begingroup$
There aren't $2^5$ subsets of size $5$...there are $binom 85$. And why would the number of subsets of size $5$ plus the number of size $4$ equal the total number of subsets?
$endgroup$
– lulu
Dec 14 '18 at 17:06












1 Answer
1






active

oldest

votes


















1












$begingroup$

Hint: Make a grid where the rows are labeled one to eight, and the columns are labeled with the subsets. Place a check mark in a box if the subset at that column contains the number at that row. Then every row has three check marks, and every column has four...






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Do you mention $70$ columns ...
    $endgroup$
    – user376343
    Dec 14 '18 at 17:21










  • $begingroup$
    No, there is only a column for each subset being considered. @user376343
    $endgroup$
    – Mike Earnest
    Dec 14 '18 at 17:22










  • $begingroup$
    I was thinking of 4-element subsets, total number. Because at the beginning we don't know the convenient collection of subsets.
    $endgroup$
    – user376343
    Dec 14 '18 at 17:26











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1 Answer
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1 Answer
1






active

oldest

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active

oldest

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active

oldest

votes









1












$begingroup$

Hint: Make a grid where the rows are labeled one to eight, and the columns are labeled with the subsets. Place a check mark in a box if the subset at that column contains the number at that row. Then every row has three check marks, and every column has four...






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Do you mention $70$ columns ...
    $endgroup$
    – user376343
    Dec 14 '18 at 17:21










  • $begingroup$
    No, there is only a column for each subset being considered. @user376343
    $endgroup$
    – Mike Earnest
    Dec 14 '18 at 17:22










  • $begingroup$
    I was thinking of 4-element subsets, total number. Because at the beginning we don't know the convenient collection of subsets.
    $endgroup$
    – user376343
    Dec 14 '18 at 17:26
















1












$begingroup$

Hint: Make a grid where the rows are labeled one to eight, and the columns are labeled with the subsets. Place a check mark in a box if the subset at that column contains the number at that row. Then every row has three check marks, and every column has four...






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Do you mention $70$ columns ...
    $endgroup$
    – user376343
    Dec 14 '18 at 17:21










  • $begingroup$
    No, there is only a column for each subset being considered. @user376343
    $endgroup$
    – Mike Earnest
    Dec 14 '18 at 17:22










  • $begingroup$
    I was thinking of 4-element subsets, total number. Because at the beginning we don't know the convenient collection of subsets.
    $endgroup$
    – user376343
    Dec 14 '18 at 17:26














1












1








1





$begingroup$

Hint: Make a grid where the rows are labeled one to eight, and the columns are labeled with the subsets. Place a check mark in a box if the subset at that column contains the number at that row. Then every row has three check marks, and every column has four...






share|cite|improve this answer









$endgroup$



Hint: Make a grid where the rows are labeled one to eight, and the columns are labeled with the subsets. Place a check mark in a box if the subset at that column contains the number at that row. Then every row has three check marks, and every column has four...







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Dec 14 '18 at 17:12









Mike EarnestMike Earnest

22.6k12051




22.6k12051












  • $begingroup$
    Do you mention $70$ columns ...
    $endgroup$
    – user376343
    Dec 14 '18 at 17:21










  • $begingroup$
    No, there is only a column for each subset being considered. @user376343
    $endgroup$
    – Mike Earnest
    Dec 14 '18 at 17:22










  • $begingroup$
    I was thinking of 4-element subsets, total number. Because at the beginning we don't know the convenient collection of subsets.
    $endgroup$
    – user376343
    Dec 14 '18 at 17:26


















  • $begingroup$
    Do you mention $70$ columns ...
    $endgroup$
    – user376343
    Dec 14 '18 at 17:21










  • $begingroup$
    No, there is only a column for each subset being considered. @user376343
    $endgroup$
    – Mike Earnest
    Dec 14 '18 at 17:22










  • $begingroup$
    I was thinking of 4-element subsets, total number. Because at the beginning we don't know the convenient collection of subsets.
    $endgroup$
    – user376343
    Dec 14 '18 at 17:26
















$begingroup$
Do you mention $70$ columns ...
$endgroup$
– user376343
Dec 14 '18 at 17:21




$begingroup$
Do you mention $70$ columns ...
$endgroup$
– user376343
Dec 14 '18 at 17:21












$begingroup$
No, there is only a column for each subset being considered. @user376343
$endgroup$
– Mike Earnest
Dec 14 '18 at 17:22




$begingroup$
No, there is only a column for each subset being considered. @user376343
$endgroup$
– Mike Earnest
Dec 14 '18 at 17:22












$begingroup$
I was thinking of 4-element subsets, total number. Because at the beginning we don't know the convenient collection of subsets.
$endgroup$
– user376343
Dec 14 '18 at 17:26




$begingroup$
I was thinking of 4-element subsets, total number. Because at the beginning we don't know the convenient collection of subsets.
$endgroup$
– user376343
Dec 14 '18 at 17:26


















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