Date: Thu, 25 Apr 1996 17:38:41 +0100
Reply-To: John Whittington <johnw@MAG-NET.CO.UK>
Sender: "SAS(r) Discussion" <SAS-L@UGA.CC.UGA.EDU>
From: John Whittington <johnw@MAG-NET.CO.UK>
Subject: Re: basic stats dumb question
On Thu, 25 Apr 1996, GERALD ZUCKIER <ZUCKIER@CHIME.ORG> wrote:
>First they ask me how many different subsets can I get out of a set with N
>members, where order is not important, and after (too much) thought I was able
>to come back with 2^N different subsets, including the null set. Now they want
>to know how many different subsets, where order IS important. I did a lot of
>scribbling and can get it down to a sort of recursive function, but is there a
>simple answer to this question? Thanks.
Not dumb at all (I thought I was dumb, too, when I first encountered it!) -
this is one of those things which sounds as if it ought to be totally
straightforward, but isn't. There may be a closed form solution but, if so,
I am unaware of it. As I'm sure you've figured, one has to deal separately
with subsets of each 'size' (number of members) - the number of possible
subsets (order being important) of size R from a set of N is obviously N! /
(N-R)! and one 'simply' has to sum this over all values of R from 1 to N
(remembering, which I usually forget, that 0!=1 :-).
John
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