Prove that:
(I can't prove without binomial coefficient.)
$ \big(m+n\big)!\over m!n!$ is a natural number
you can use : formula for the largest power of a prime dividing a factorial $ n!=p_1^\alpha* p_2^\beta* ... $ $ \alpha= \lfloor n/p \rfloor + \lfloor n/p^2 \rfloor+... $