Re: k-permutations enumeration

*To*: mathgroup at smc.vnet.net*Subject*: [mg116314] Re: k-permutations enumeration*From*: Ray Koopman <koopman at sfu.ca>*Date*: Fri, 11 Feb 2011 04:12:18 -0500 (EST)*References*: <ij0eaq$9eo$1@smc.vnet.net>

On Feb 10, 2:23 am, Michal Kvasnicka <michal.kvasni... at gmail.com> wrote: > 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? k = 15; r = {4,5,8,3}; Tr[Multinomial@@@Select[Tuples[Range/@r],Tr@#==k&]] 184984800