Question

The number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one balls is

Answer 1

Possible combination are $1,1,3$ and $2,2,1$

The number of required ways$=\frac{5!}{{\left(1!\right)}^2\times 3!\left(2!\right)}\times 3!+\frac{5!}{\left(2!\right)\times 1!\left(2!\right)}\times 3!$

$=60+90=150$ answer.