```Date: Oct 14, 2001 11:55 PM
Author: Entropix
Subject: Re: Homework question: permutations

"Fred Galvin" <galvin@math.ukans.edu> wrote in messagenews://Pine.LNX.4.21.0110132333410.20087-100000@titania.math.ukans.edu...> On Sun, 14 Oct 2001, Effusive wrote:>> > "Fred Galvin" <galvin@math.ukans.edu> wrote in message> > news://Pine.LNX.4.21.0110131534290.10973-100000@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>> How do you get 2/3?? There are 3! = 6 permutations of {1,2,3}; 3 of> them have order 2 (the transpositions), and the other 3 have order 1> or 3.>> Permutation  Order> (1)(2)(3)    1> (1,2)(3)     2> (1,3)(2)     2> (1)(2,3)     2> (1,2,3)      3> (1,3,2)      3Lol! Sorry. I read something wrong; I won't post when I'm tired anymore.-- Entropix
```