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

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Entropix

Posts: 40
Registered: 12/13/04
Re: Homework question: permutations
Posted: Oct 13, 2001 10:20 PM
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"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

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?
>
>









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