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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 ?___

A
75
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B
150
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C
210
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D
243
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Solution

The correct option is B 150
Objects Groups Objects Groups
Distinct Distinct Identical Identical
Distinct Identical Identical Distinct
Description of Situation Here, 5 distinct balls are distributed amongst 3 persons so that each gets at least one ball. i.e. Distinct Distinct
So, we should make cases
Case IABC113}Case IIABC122}
Number of ways to distribute 5 balls
=(5C1.4C1.3C3×3!2!)+(5C1.4C2.2C2×3!2!)=60+90=150

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