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Unformatted text preview: mutations in which she is part of a couple. Otherwise, there are
permutations in which she is part of two couples and
permutations in
which she is part of one couple. There are
permutations with her in that seat, so
the expected number of couples containing a randomly chosen woman is This simplifies to There are women, so by linearity of expectation the expected number of couples is (As a partial check against obvious errors, notice that this expression is unchanged if we
interchange the rôles of and , as it obviously should be.)
a nsw ered Ma r 21 a t 1 5:1 2
Bria n M. Scott
138k 16 117 243 ma th.sta c ke xc ha nge .c om/que stions/336896/c ounting c ouple s 1/4 3/27/13 pr oba bility  Counting Couple s  Ma the ma tic s This problem may also be solved using generating functions. Let
be the number of
sequences of length with couples where the last person is male. Similarly, let
be the
number of sequences of length with couples where the last person is female.
This gives the following relations: Here the variable r...
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This document was uploaded on 02/23/2014 for the course CS 214 at Rutgers.
 Spring '14
 Exams, Cs214, Projects

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