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Question

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 
  1. 75
  2. 150
  3. 210
  4. 243


Solution

The correct option is B 150
Each person gets at lest one ball.
3 persons can have 5 balls in the following systems  
PersonIIIIIINo. of balls113              or        PersonIIIIIINo. of balls122
The number of ways to distribute the balls in first system 
= 5C1× 4C1× 3C3 
Also 3, persons having 1,1 and 3 balls can be arranged in 3!2!ways.
= 5C1× 4C1× 3C3×3!2!=60
Similarly the total no.of ways to distribute 1,2,2 balls to the three perrsons = 5C1× 4C2× 2C2×3!2!=90
The required numbers of ways = 60 + 90 = 150.

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