In how many ways can 6 pictures be hung from 4 picture nails on a wall?

To find: number of ways of hanging 6 pictures on 4 picture nails.

There are 6 pictures to be placed in 4 places.

Formula:

Number of permutations of $n$ distinct objects among $r$ different places, where repetition is not allowed, is

$P(n, r)=n ! /(n-r) !$

Therefore, a permutation of 6 different objects in 4 places is

$P(6,4)=\frac{\frac{6 !}{(6-4) !}}{2 !}=\frac{6 !}{2 !}=\frac{720}{2}=360$

This can be done by 360 ways