Combinations with repetition

The calculator finds the number of combinations of the k-th class from n elements with repetition. A combination with repetition of k objects from n is a way of selecting k objects from a list of n. The order of selection does not matter and each object can be selected more than once (repeated).



Ck(n)=(kn+k1)  n=10 k=4  C4(10)=C4(10+41)=C4(13)=(413)=4!(134)!13!=432113121110=715

The number of combinations with repetition: 715

A bit of theory - the foundation of combinatorics

Combinations with repeat

Here we select k element groups from n elements, regardless of the order, and the elements can be repeated. k is logically greater than n (otherwise, we would get ordinary combinations). Their count is:


Explanation of the formula - the number of combinations with repetition is equal to the number of locations of n − 1 separators on n-1 + k places. A typical example is: we go to the store to buy 6 chocolates. They offer only 3 species. How many options do we have? k = 6, n = 3.

Foundation of combinatorics in word problems

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