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AIEEE 2012

JEE Main 2012 Mathematics question on Permutations and Combinations

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. A.
    75
  2. B.
    150
  3. C.
    210
  4. D.
    243
Show answer and solution

Correct option: B

Solution

Using inclusion-exclusion, the number of surjective (onto) functions from 5 balls to 3 persons is:

35 - C(3,1)·25 + C(3,2)·15 = 243 - 3(32) + 3(1) = 243 - 96 + 3 = 150.

This counts all distributions where every person gets at least one ball, giving 150.

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