Binomial Coeffients

Apr 2010
3
0
I have the following in my book:

"\(\displaystyle (N K ) = n! / k! (n - k)!\)

This formula is symmetric in k and n-k:

\(\displaystyle ( N K ) = ( n / n - k)\)"

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?

Can you explain it please?
 

Plato

MHF Helper
Aug 2006
22,461
8,632
\(\displaystyle \binom{N}{K}=\frac{N!}{K!(N-K)!}\)
\(\displaystyle \binom{N}{N-K}=\frac{N!}{(N-K)![N-(N-K)]!}=\frac{N!}{(N-K)!(K)!}\)
 
Apr 2010
3
0
So how can you just add a factorial to the second equation??
 

Plato

MHF Helper
Aug 2006
22,461
8,632
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.