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

 Messages: [ Previous | Next ]
 Fred Galvin Posts: 1,758 Registered: 12/6/04
Homework question: permutations
Posted: Oct 13, 2001 4:45 PM

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?

Date Subject Author
10/13/01 Fred Galvin
10/13/01 Entropix
10/14/01 Fred Galvin
10/14/01 Entropix
10/15/01 Robin Chapman
10/15/01 Robin Chapman
10/16/01 Fred Galvin
10/18/01 Jim Ferry
10/18/01 Fred Galvin
10/19/01 Jim Ferry
10/19/01 Fred Galvin
10/21/01 ayatollah potassium
10/20/01 ayatollah potassium