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Maths Exercices

Combinations with repetition

An m-combination with repetition allowed, or a multiset of size m, chosen from a set of n elements, is an unordered selection of elements with repetition allowed.

The number of m-combinations with repetition allowed that can be selected from n elements is
C(n + m - 1; m), that is:

 

There are three flavors of icecream: chocolate, lemon and vanilla. You can have three scoops. How many variations will there be?
Lets use letters for the flavors: {c, l, v}.

Possible selections are:
{c,c,c} {c,c,l} {c,c,v} {c,l,v} {l,l,l} {l,l,c} {l,l,v} {v,v,v} {v,v,c} {v,v,l}

Using the formula:


Enter any numbers n and m you want and the computer will calculate for you the number of combinations with repetition.
Enter n = m =
C(n+m-1,m)=