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

'5' balls to be distributed among '3'.Total number of distribution possible=3⁵.Of these distributions, there are cases when one person does not get any ball.Number of such cases=3C1×(2⁵)=96.Also, there are cases when one gets all.Number of such cases=3C1=3.So, distributions such that each gets at least 1 is 3⁵ - 96 = 243 - 96 = 150.