k-permutations enumeration

*To*: mathgroup at smc.vnet.net*Subject*: [mg116305] k-permutations enumeration*From*: Michal Kvasnicka <michal.kvasnicka at gmail.com>*Date*: Thu, 10 Feb 2011 05:23:48 -0500 (EST)

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? Example: 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? Any Mathematica code?