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
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
A singing choir of 4 children is to be formed. The selection pool consists of 8 siblings pairs. In how many ways can a
This topic has expert replies
-
BTGmoderatorDC
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
-
regor60
- Master | Next Rank: 500 Posts
- Posts: 415
- Joined: Thu Oct 15, 2009 11:52 am
- Thanked: 27 times
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
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
