VJesus12 wrote: ↑Thu Jun 24, 2021 11:42 am
If there are \(4\) pairs of twins, and a committee will be formed with \(3\) members. In how many ways this committee formed in a way that no siblings in a group?
A. 32
B. 24
C. 56
D. 44
E. 40
Answer:
A
Source: GMAT Prep
Take the task of selecting the 3 committee members and
break it into stages.
Stage 1: Select the 3 twin pairs from which we will select 1 sibling each.
There are 4 pairs of twins, and we must select 3 pairs. Since the order in which we select the 3 pairs does not matter, we can use COMBINATIONS
We can select 3 pairs from 4 pairs in 4C3 ways (
4 ways)
Stage 2: Take one of the 3 selected pairs and choose 1 person to be on the committee.
There are 2 people in the twin pair, so this stage can be accomplished in
2 ways.
Stage 3: Take another of the 3 selected pairs and choose 1 person to be on the committee.
There are 2 people in the twin pair, so this stage can be accomplished in
2 ways.
Stage 4: Take the last of the 3 selected pairs and choose 1 person to be on the committee.
There are 2 people in the twin pair, so this stage can be accomplished in
2 ways.
By the Fundamental Counting Principle (FCP) we can complete all 4 stages (and thus create a 3-person committee) in
(4)(2)(2)(2) ways (= 32 ways)
Answer = A
