Question

In how many ways 7 pictures can be hung from 5 picture nails on a wall ?

Answer 1

The number of ways in which $7$ pictures can be hung from $5$ picture nails on a wall is the same as the number of arrangements of 7 things, taking 5 at a time.

Hence, the required number = $7_{P_5}=\frac{7!}{(7-5)!}=\frac{7!}{2!}=2520$