Note: I tried asking this on math.stackexchange (here), but didn't really receive an answer - so I figured this might be the right place.
How can I find the number of k-permutations of n objects, where there are x types of objects, and r1, r2, r3 ... rx give the number of each type of object?
I have 20 letters from the alphabet. There are some duplicates - 4 of them are a, 5 of them are b, 8 of them are c, and 3 are d. How many unique 15-letter permutations can I make?
In the example:
n = 20
k = 15
x = 4
r1 = 4, r2 = 5, r3 = 8, r4 = 3
Furthermore, if there isn't a straightforward solution: how efficiently can this problem be solved?