
Re: Homework question: permutations
Posted:
Oct 13, 2001 10:20 PM


"Fred Galvin" <galvin@math.ukans.edu> wrote in message news://Pine.LNX.4.21.0110131534290.10973100000@titania.math.ukans.edu... > 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. >
?? n = 2
{1, 2} Probability a random element has odd order is 1/2
n + 1 = 3
{1, 2, 3} Probability a random element has odd order is 2/3
These aren't equivalent.... Am _I_ missing something?
 Entropix
> 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? > >

