# Binomial Coeffients

#### tbone2500

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?

#### Plato

MHF Helper
$$\displaystyle \binom{N}{K}=\frac{N!}{K!(N-K)!}$$
$$\displaystyle \binom{N}{N-K}=\frac{N!}{(N-K)![N-(N-K)]!}=\frac{N!}{(N-K)!(K)!}$$

#### tbone2500

So how can you just add a factorial to the second equation??

#### Plato

MHF Helper
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.