Re: (1 Combination 2) = 0 -- Better explanation?

On 7/14/2024 2:57 PM, HenHanna wrote:

Python says:  (1 Combination 2) = 0

         Ok... It's Impossible (to do).

              ------- is there a Better explanation?



(5 Combination 0) = 1  <---- This is explained by  Comb(5,0)=Comb(5,5)

                                      in general:   Comb(N,r)=Comb(N,N-r)

_______________________________________

from math import comb

for i in range(6):      print( comb(5,i) )

print( comb(1,2)  )

Let combination of n things taken m at a time be represented by [n,m].
Then [n,m] = [n,n-m] as you correctly note above. Further, we have the
computational formula [n,m] = n!/(m!(n-m)!) where x!  is simply x
factorial. So [1,2] = 1!/(2!((-1)!)), or 1/2 divided by (-1)!. However
factorial of a negative integer is, by convention, an infinite value so
[1.2] = 0.
--
Jeff Barnett