# Number of ways

How many permutations (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 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.

How many permutations (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 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.
Problems like the two you pose are generally solved using generating functions: exponential generating functions in the case of permutations (your first question) and ordinary generating functions in the case of combinations (your second question). When the problem is sufficiently complicated or general, you may be able to find the generating function which "solves" the problem even though you are not able to get a formula for the "number of ways". There is still value in the generating function in such a case, because you may be able to discover facts about the problem that are not obvious, such as recurrences or asymptotic behavior of the solution.

See http://en.wikipedia.org/wiki/Generating_function