Possible Duplicate:
Proof of a combination identity:$\sum \limits_{j=0}^n{(-1)^j{{n}\choose{j}}\left(1-\frac{j}{n}\right)^n}=\frac{n!}{n^n}$
Prove that product of $n(n-1)(n-2)\dots(2)(1)$ i.e.
$$n! = \sum_{i=0}^{n-1}{n \choose i}(n-i)^n (-1)^i$$
Possible Duplicate:
Proof of a combination identity:$\sum \limits_{j=0}^n{(-1)^j{{n}\choose{j}}\left(1-\frac{j}{n}\right)^n}=\frac{n!}{n^n}$
Prove that product of $n(n-1)(n-2)\dots(2)(1)$ i.e.
$$n! = \sum_{i=0}^{n-1}{n \choose i}(n-i)^n (-1)^i$$