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MathGroup Archive 2011

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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?


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