Question

If no digit may be used more than once, how many 5-digit numbers can be formed using only the digits 3, 8, 1, 2, 5, and 7?

Answer 1

The number of permutations of $m(0\leq m\leq n)$ objects from n objects is

$P(m,n)=\frac{n!}{(n-m)!}$

Here 5 digits are chosen from 6 digits without replacement (order important).

The number of 5 digit numbers that can be formed is

$\frac{6!}{(6-5)!} =6!=720$