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

Step-by-step solution

Each person gets at least one ball. 3 Persons can have 5 balls as follow. array |c|c|c| Person & No. of balls & No. of balls I & 1 & 1 II & 1 & 2 III & 3 & 2 array The number of ways to distribute balls 1,1,3 in first to three persons = ⁵ C ₁ ⁴ C ₁ ³ C ₃ Also 3 , persons having 1,1 and 3 balls can be arranged in 3 ! 2 ! ways. Total no. of ways to distribute 1,1,3 balls to the three persons = ⁵ C ₁ ⁴ C ₁ ³ C ₃ 3 ! 2 ! =60 Similarly, total no. of ways to distribute 1,2,2 balls to three persons = ⁵ C ₁ ⁴ C ₂ ² C ₂ 3 !