Prove that If $p$ is prime s.t. $0Prove that If $p$ is prime s.t. $0<n\leq p$ , then $p|[{p! \over {(p-n)!(n)!}}]$.
 I know that if $p|q$ , then $q=kp$, for some integer number $k$.
 But I don’t know how to prove that $p$ divided like above.
Is it working to use proof by induction? 

Hint (assuming you have $n<p$): Show that $p$ does divide the numerator, but doesn't divide either of the factors in the denominator.
