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 $$ n!=p_1^\alpha* p_2^\beta* ... $$ $$ \alpha= \lfloor n/p \rfloor + \lfloor n/p^2 \rfloor+... $$