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Topic: Homework question: permutations
Replies: 12   Last Post: Oct 21, 2001 8:04 PM

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Fred Galvin

Posts: 1,758
Registered: 12/6/04
Homework question: permutations
Posted: Oct 13, 2001 4:45 PM
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S_n is the group of all permutations of {1,2,...,n}.

If n is an even number, the following probabilities are equal:
(a) the probability that a random element of S_n has odd order;
(b) the probability that a random element of S_{n+1} has odd order;
(c) the probability of getting equal numbers of heads and tails in n
independent tosses of a fair coin.

This came up in a homework problem in my combinatorics class. It's
easy enough to verify the equalities by mindless computation with
generating functions, but I think they must have a simple explanation.
What is it?

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