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When k = N this is easy and is equal to N!/(n1!n2!...nr!)

The following question would be then how many combinations (when objects are not all distinct) of size k can be created from a set of size N composed of n1, n2,n3,...,nr parts?

When all objects are distinct we know that this would be N!/((N-k)!k!)

Looking through the combinatorics section of my statistics book they don't mention these seemingly important situations.