Question

Let k and n be positive integers, with k < n. Write
n!
--
k!
without using factorials;
simplify your answer.

Answer 1

\[\frac{n!}{k!}\]

Answer 2

n! = n(n-1)(n-2)....(n+k-n+1)k!
or you can take n-k= p as n>k
n!= (p+k)! = (p+k)(p+k-1).....(p+k-(p-1))k!
then put p= n-k