Gifts

Probability Level 3

Uncle Paul brought five different gifts, including a doll, to distribute among his nieces Anne, Bruna, Daniela and Cecily. How many ways can he distribute gifts among the nieces so that all earning at least one gift and the doll is given to Anne?

120 32 60 72

Victor Paes Plinio by Victor Paes Plinio , 21, Brazil

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1 solution

Vikram Kumar
Apr 8, 2014

There can be 2 different ways to think about the distribution of gifts :-

  1. Anne gets only the doll and the rest three gets 2,1,1 gifts or 1,2,1 gifts or 1,1,2 gifts respectively which gives 

      3*( 4C2 * 2C1 * 1C1) ways = 36 ways. [As (4C2 * 2C1 * 1C1)=(4C1 * 3C2 * 1C1)=(4C1 * 3C1 * 2C2)]
  2. Anne gets 2 gifts out of which one is the doll . Now the remaining 4 gifts can be distributed among the four nieces in 4! ways = 24 ways.

This gives the total number of ways as 36 + 24 = 60 ways

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