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



"Fred Galvin" <galvin@math.ukans.edu> wrote in message
news://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)      3

Lol! Sorry. I read something wrong; I won't post when I'm tired anymore.

-- Entropix