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From: Ben Bacarisse <ben@bsb.me.uk>
Newsgroups: comp.lang.python,sci.math,sci.lang
Subject: Re: (1 Combination 2) = 0 -- Better explanation?
Date: Tue, 16 Jul 2024 12:35:33 +0100
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HenHanna <HenHanna@devnull.tb> writes:

> Python says:  (1 Combination 2) = 0
>         Ok... It's Impossible (to do).
>              ------- is there a Better explanation?

JB has given you an explanation to do with generalising the algebraic
equations, but there are also simple explanations from first principles.

> (5 Combination 0) = 1  <---- This is explained by  Comb(5,0)=Comb(5,5)
>                                      in general:   Comb(N,r)=Comb(N,N-r)

I'll write |[5,0]| for this.  In general |[n,m]| is the number of
m-element subsets of a typical set of n elements.  So how many
zero-element subsets of such a set are there?  Just 1.  |[n,0]| = 1.

And how many 2-element subsets of a 1-element set are there?  0, so
|[1,2]| = 0.

-- 
Ben.