Mixing
Number of ways to pick an equal number of elements from two sets?
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There are two groups such that one group contains $m$ elements and another group contains $n$ elements. We have to find number of ways to pick same number of elements from both the groups.
My approach is
$1+dbinom m1.dbinom n1+dbinom m2 . dbinom n2 +.... $upto $dbinom mm$ or $dbinom nn$ whatever is smaller.
Is there any faster way to do the same?
Example:
$3$ and $2$
$1+dbinom 31.dbinom 21+dbinom 32 . dbinom 22=10$ ways
combinatorics permutations
edited yesterday
SmarthBansal
36412
asked yesterday
Sagar Sharma
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up vote
2
down vote
favorite
There are two groups such that one group contains $m$ elements and another group contains $n$ elements. We have to find number of ways to pick same number of elements from both the groups.
My approach is
$1+dbinom m1.dbinom n1+dbinom m2 . dbinom n2 +.... $upto $dbinom mm$ or $dbinom nn$ whatever is smaller.
Is there any faster way to do the same?
Example:
$3$ and $2$
$1+dbinom 31.dbinom 21+dbinom 32 . dbinom 22=10$ ways
combinatorics permutations
edited yesterday
SmarthBansal
36412
asked yesterday
Sagar Sharma
161
New contributor
Sagar Sharma is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
There are two groups such that one group contains $m$ elements and another group contains $n$ elements. We have to find number of ways to pick same number of elements from both the groups.
My approach is
$1+dbinom m1.dbinom n1+dbinom m2 . dbinom n2 +.... $upto $dbinom mm$ or $dbinom nn$ whatever is smaller.
Is there any faster way to do the same?
Example:
$3$ and $2$
$1+dbinom 31.dbinom 21+dbinom 32 . dbinom 22=10$ ways
combinatorics permutations
edited yesterday
SmarthBansal
36412
asked yesterday
Sagar Sharma
161
New contributor
Sagar Sharma is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
There are two groups such that one group contains $m$ elements and another group contains $n$ elements. We have to find number of ways to pick same number of elements from both the groups.
My approach is
$1+dbinom m1.dbinom n1+dbinom m2 . dbinom n2 +.... $upto $dbinom mm$ or $dbinom nn$ whatever is smaller.
Is there any faster way to do the same?
Example:
$3$ and $2$
$1+dbinom 31.dbinom 21+dbinom 32 . dbinom 22=10$ ways
combinatorics permutations
combinatorics permutations
edited yesterday
SmarthBansal
36412
asked yesterday
Sagar Sharma
161
New contributor
Sagar Sharma is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited yesterday
SmarthBansal
36412
asked yesterday
Sagar Sharma
161
New contributor
Sagar Sharma is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited yesterday
SmarthBansal
36412
edited yesterday
SmarthBansal
36412
edited yesterday
SmarthBansal
36412
36412
asked yesterday
Sagar Sharma
161
New contributor
Sagar Sharma is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
Sagar Sharma
161
asked yesterday
Sagar Sharma
161
161
New contributor
Sagar Sharma is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Sagar Sharma is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Sagar Sharma is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
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Sagar Sharma is a new contributor. Be nice, and check out our Code of Conduct.
Sagar Sharma is a new contributor. Be nice, and check out our Code of Conduct.
Sagar Sharma is a new contributor. Be nice, and check out our Code of Conduct.
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