The number of ways in which 5 pictures can be hung from 7 picture nails on the wall is 

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

Hence, the required number ${=}^7{P}_5=\frac{7!}{2!}=2520$