
Re: Homework question: permutations
Posted:
Oct 14, 2001 11:55 PM


"Fred Galvin" <galvin@math.ukans.edu> wrote in message news://Pine.LNX.4.21.0110132333410.20087100000@titania.math.ukans.edu... > On Sun, 14 Oct 2001, Effusive wrote: > > > "Fred Galvin" <galvin@math.ukans.edu> wrote in message > > news://Pine.LNX.4.21.0110131534290.10973100000@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 > > 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

