- #1
Government$
- 87
- 1
Homework Statement
Prove the following:
[itex]\frac{n!}{m!(n-m)!} = \frac{n!}{(m-2)!(n-m + 2)!} + 2* \frac{(n-1)!}{(m-1)!(n-m)!} + \frac{(n-2)!}{(m-2)!(n-m)!} [/itex]
The Attempt at a Solution
I tried writing following
[itex]\frac{n!}{m!(n-m)!} = \frac{n!}{m!(n-m)!}(\frac{m(m-1)}{(n-m + 2)(n-m + 1)} + \frac{2m}{n} + \frac{m(m-1)}{n(n-1)} [/itex])
Now i should get [itex]\frac{m(m-1)}{(n-m + 2)(n-m + 1)} + \frac{2m}{n} + \frac{m(m-1)}{n(n-1)} = 1[/itex]
but i don't get 1. Any other ideas?