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

Step-by-step solution

We know that total number of ways of distributing n distinct things among m persons such that each person gets at least one thing = m n − C m 1 . ( m − 1 ) n + C m 2 ( m − 2 ) n − C m 3 ( m − 3 ) n + ..... So the required total number of ways = 3 5 − C 3 1 .2 5 + C 3 2 .1 5 . = 243 − 96 + 3 = 150