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 Arithmetics Signed numbers Divisibility Decimals Fractions Percentages Proporcional reasoning Mixture problems Prime numbers Factoring Prime factorization GCF LCM Radicals Exponential expressions Uniform Motion Problems Ratio Proportions Direct variation Inverse variation
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 Factorial Variations without repetition Variations with repetition Permutations with repetition Permutations without repetition Exercises Circular permutations Binomial coefficient Combinations with repetition Combinations without repetition
 Arithmetic mean

 Combinatorics 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)=