math questions

[Sherry Listgarten]

I think he means unordered groups: "n choose k" is n! / ( k! * (n-k)!)

(For those who don't know, n! is the product of the first n numbers
(1*2*3*...*n) = "n factorial".)

This is the number of groups of k items from n (distinct) elements.

So, for example, the number of groups of 2 items from 4 distinct items is
4!/2!2! = 24/4=6: {12}{13}{14}{23}{24}{34}

There's a short form for the sum, but I forget it. Lemme think about it. The
full sum (k = 1..n) is 2^n.

-- Sherry.

> -----Original Message-----
> From: Russell Turpin [mailto:deafbox@hotmail.com]
> Sent: Friday, November 02, 2001 6:02 AM
> To: fork@xent.com
> Subject: Re: math questions
> 
> 
> Clay asks:
> >What are the formulae for calculating the number of groups 
> of size G within 
> >a total group of N, and the number of groups of size G or smaller.
> 
> If I'm not thinking too fast, the first number is "100
> choose 12", which is:
> 
>      N!/(N-G)! = (100!)/(100-12)! = 503153364153791070720000
> 
> The second number is just "100 choose 12" plus "100
> choose 11" plus, etc., or:
> 
>      sum N!/(N-k)!, for 1<=k<=G
> 
> These numbers grow very quickly.
> 
> Next, you'll want to know Ackermann's function.
> 
> Russell
> 
> 
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