Homework Help: Binomial theorem

1. Jun 11, 2014

Jef123

1. How do you get n!/(k-1)!(n-k+1)! from $$\begin{pmatrix} n\\k-1 \end{pmatrix}$$

I thought it would be n!/(k-1)!(n-k-1)! where the n-k+1 on the bottom of the fraction would be a n-k-1 instead. I don't understand why there is a "+1" wouldn't you just replace k with k-1 in the binomial formula?

2. Jun 11, 2014

whoareyou

$$\binom{n}{k-1}=\frac {n!}{(k-1)!(n-(k-1))!}=\frac{n!}{(k-1)!(n-k+1))!}$$

3. Jun 11, 2014

Jef123

I just got it after i typed that out. I cant believe i didnt notice that

4. Jul 17, 2014

Alicelewis11

Binomial theorem use for different purposes. The above person share write formula.