Number of unique combinations of $k$ items from a set $S$ of $n$ items, with repetitions in S. ($k<n$)
What would be the formula for the number of unique combinations of $k$ items from a set $S$ of $n$ items, with repetitions in S. ($k<n$) (Order does not matter)
Example #1:
$$ S=2,2,3,4,4,8 $$
$$ k=2 $$
$$(2,2)(2,3)(2,4)(2,8)(3,4)(3,8)(4,4)(4,8)$$
Example #2:
$$ S=3,5,5,5,5,5,5,7,9,11,15,15$$
$$ k=2 $$
$$(3,5)(3,7)(3,9)(3,11)(3,15)(5,5)(5,7)(5,9)(5,11)$$
$$(5,15)(7,9)(7,11)(7,15)(9,11)(9,15)(11,15)(15,15)$$
combinatorics
asked Nov 27 at 4:09
François Huppé
324111
add a comment |
What would be the formula for the number of unique combinations of $k$ items from a set $S$ of $n$ items, with repetitions in S. ($k<n$) (Order does not matter)
Example #1:
$$ S=2,2,3,4,4,8 $$
$$ k=2 $$
$$(2,2)(2,3)(2,4)(2,8)(3,4)(3,8)(4,4)(4,8)$$
Example #2:
$$ S=3,5,5,5,5,5,5,7,9,11,15,15$$
$$ k=2 $$
$$(3,5)(3,7)(3,9)(3,11)(3,15)(5,5)(5,7)(5,9)(5,11)$$
$$(5,15)(7,9)(7,11)(7,15)(9,11)(9,15)(11,15)(15,15)$$
combinatorics
asked Nov 27 at 4:09
François Huppé
324111
Any such formula would require first turning $S$ from a multiset into a set
– user25959
Nov 27 at 4:14
What if the number of unique items in S is also known ?
– François Huppé
Nov 27 at 4:22
en.wikipedia.org/wiki/…
– user25959
Nov 27 at 4:23
add a comment |
What would be the formula for the number of unique combinations of $k$ items from a set $S$ of $n$ items, with repetitions in S. ($k<n$) (Order does not matter)
Example #1:
$$ S=2,2,3,4,4,8 $$
$$ k=2 $$
$$(2,2)(2,3)(2,4)(2,8)(3,4)(3,8)(4,4)(4,8)$$
Example #2:
$$ S=3,5,5,5,5,5,5,7,9,11,15,15$$
$$ k=2 $$
$$(3,5)(3,7)(3,9)(3,11)(3,15)(5,5)(5,7)(5,9)(5,11)$$
$$(5,15)(7,9)(7,11)(7,15)(9,11)(9,15)(11,15)(15,15)$$
combinatorics
asked Nov 27 at 4:09
François Huppé
324111
What would be the formula for the number of unique combinations of $k$ items from a set $S$ of $n$ items, with repetitions in S. ($k<n$) (Order does not matter)
Example #1:
$$ S=2,2,3,4,4,8 $$
$$ k=2 $$
$$(2,2)(2,3)(2,4)(2,8)(3,4)(3,8)(4,4)(4,8)$$
Example #2:
$$ S=3,5,5,5,5,5,5,7,9,11,15,15$$
$$ k=2 $$
$$(3,5)(3,7)(3,9)(3,11)(3,15)(5,5)(5,7)(5,9)(5,11)$$
$$(5,15)(7,9)(7,11)(7,15)(9,11)(9,15)(11,15)(15,15)$$
combinatorics
combinatorics
asked Nov 27 at 4:09
François Huppé
324111
asked Nov 27 at 4:09
François Huppé
324111
asked Nov 27 at 4:09
François Huppé
324111
asked Nov 27 at 4:09
François Huppé
324111
asked Nov 27 at 4:09
François Huppé
324111
324111
Any such formula would require first turning $S$ from a multiset into a set
– user25959
Nov 27 at 4:14
What if the number of unique items in S is also known ?
– François Huppé
Nov 27 at 4:22
en.wikipedia.org/wiki/…
– user25959
Nov 27 at 4:23
add a comment |
Any such formula would require first turning $S$ from a multiset into a set
– user25959
Nov 27 at 4:14
What if the number of unique items in S is also known ?
– François Huppé
Nov 27 at 4:22
en.wikipedia.org/wiki/…
– user25959
Nov 27 at 4:23
Any such formula would require first turning $S$ from a multiset into a set
– user25959
Nov 27 at 4:14
Any such formula would require first turning $S$ from a multiset into a set
– user25959
Nov 27 at 4:14
What if the number of unique items in S is also known ?
– François Huppé
Nov 27 at 4:22
What if the number of unique items in S is also known ?
– François Huppé
Nov 27 at 4:22
en.wikipedia.org/wiki/…
– user25959
Nov 27 at 4:23
en.wikipedia.org/wiki/…
– user25959
Nov 27 at 4:23
add a comment |
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Any such formula would require first turning $S$ from a multiset into a set
– user25959
Nov 27 at 4:14
What if the number of unique items in S is also known ?
– François Huppé
Nov 27 at 4:22
en.wikipedia.org/wiki/…
– user25959
Nov 27 at 4:23