Boys and sisters

Probability Level 1

Sarah has 17 cousins and 3 sisters. If she and her sisters want to take 4 other boys to the dance, in how many ways can they be paired up in boy-girl pairs?


The answer is 24.

Rishik Jain by Rishik Jain , 21, India

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1 solution

Dylan Lam
Mar 2, 2016

If you got 4 girls wanting to pair up with 4 guys in how many ever ways it is needed, then the order of the couples would matter. It's just permutations. Therefore, the answer is just 4! (which would equal 24) on a calculator. Simply put, it is just 4 x 3 x 2 x 1. Otherwise you can just draw up all the possible combinations by hand (which is more time consuming).

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Meanwhile, the question is poorly worded, in my opinion. To take 4 boys from among 17 cousins is itself possible in so many ways. That is not being considered at all. So, the assumption is, they have already chosen the boys, only the matchup is to be counted. That doesn't come through clearly in the question.

Also, cousins? boys? gender breakup not given? Again misleading unnecessarily.

Rajendran Dandapani - 4 years, 2 months ago

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