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