Prove that the combination formula can be reduced to... Prove that:
$$\frac{m!}{k!(m-k)!} = \frac{m}{k}\frac{m-1}{k-1}\cdots\frac{m-k+1}{1}$$
It's quite obvious when I write down some terms, but I just don't know how to make a rigorous proof. Any hints or help are appreciated!
Thanks.

$$\frac{m!}{k!(m-k)!} =\frac{1\cdot\ 2\cdot...\cdot(m-k)\cdot(m-k+1)\cdot...\cdot m}{(1\cdot\ 2\cdot...\cdot k)(1\cdot\ 2\cdot...\cdot(m-k))}$$
