JEE Advanced · 2012 · 08 Apr 2012 · Paper 1 · Permutations and Combinations

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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
(B)150✓ Correct
(C)210
(D)243

Answer: (B)

Solution

We use the inclusion-exclusion principle. The total number of ways to distribute 5 distinct balls among 3 persons (without restriction) is

3^{5} = 243

. We subtract the cases where at least one person gets no ball:

(1 3) \cdot 2^{5} = 96

(one person gets nothing). We add back the cases where at least two persons get no ball:

(2 3) \cdot 1^{5} = 3

(two persons get nothing). By inclusion-exclusion:

243 - 96 + 3 = 150

JEE Advanced · 2012 · 08 Apr 2012 · Paper 1 · Single correct option

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