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

Options

A. 75
B. 150
C. 210
D. 243

Explanation

`because` Each person gets atleast one ball.
`therefore` 3 persons can have 5 balls in the following systems

the number of ways to distribute the balls in first system
`=.^(5)C_(1)xx.^(4)C_(1)xx.^(3)C_(3)`
`therefore` The total number of ways to distribute 1,1,3 balls to the persons`=.^(5)C_(1)xx.^(4)C_(1)xx.^(3)C_(3)xx(3!)/(2!)=60`
and the number of ways to distribute the balls in second system`=.^(5)C_(1)xx.^(4)C_(2)xx.^(2)C_(2)`
Hence, the total number of ways to distribute 1,2,2 balls to the persons `.^(5)C_(1)xx.^(4)C_(2)xx.^(2)C_(2)xx(3!)/(2!)=90`
`therefore`The required nnumber of ways`=60+90=150`