# Binomial Coeffients

• May 8th 2010, 01:08 PM
tbone2500
Binomial Coeffients
I have the following in my book:

" $(N K ) = n! / k! (n - k)!$

This formula is symmetric in k and n-k:

$( N K ) = ( n / n - k)$"

I'm trying to understand what it means with 'this formula is symmetric in n and n-k'. I have tried to look for an answer, but haven't found anything. Does anyone know what that is supposed to mean?

• May 8th 2010, 01:21 PM
Plato
$\binom{N}{K}=\frac{N!}{K!(N-K)!}$
$\binom{N}{N-K}=\frac{N!}{(N-K)![N-(N-K)]!}=\frac{N!}{(N-K)!(K)!}$
• May 8th 2010, 02:03 PM
tbone2500
So how can you just add a factorial to the second equation??
• May 8th 2010, 02:56 PM
Plato
Quote:

Originally Posted by tbone2500
So how can you just add a factorial to the second equation??

Actually it is a mere application of the combination formula and simple addition.
You are expected to know how to use both.