A singing choir of 4 children is to be formed. The selection pool consists of 8 siblings pairs. In how many ways can a

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by BTGmoderatorDC » Mon Feb 07, 2022 4:24 pm

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A singing choir of 4 children is to be formed. The selection pool consists of 8 siblings pairs. In how many ways can a choir be formed if both siblings cannot be selected together?
(A) 360
(B) 720
(C) 1120
(D) 2400
(E) 26880

OA C

Source: e-GMAT

Source: Beat The GMAT — Problem Solving | Mon Feb 07, 2022 4:24 pm

regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

Re: A singing choir of 4 children is to be formed. The selection pool consists of 8 siblings pairs. In how many ways can

by regor60 » Tue Feb 08, 2022 6:13 am

Because each child has to come from a separate sibling pair, you need to first select which pairs will be represented.

Four pairs can be selected from 8:

8!/4!4! = 70 ways

Since only one child can be selected from each pair and there are 2 ways to select which child from each pair, there are:

2^4 = 16 ways to select 4 children from the pairs excluding siblings.

Total ways: 70*16=1120,C

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