There are four distinct pairs of brothers and sisters. In how many ways can a committee of 3 be formed and not have siblings in it?
(A) 8
(B) 24
(C) 32
(D 56
(E) 80
problem solving: combinations
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- fiza gupta
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Take the task of creating a committee and break it into stages.fiza gupta wrote:There are four distinct pairs of brothers and sisters. In how many ways can a committee of 3 be formed and not have siblings in it?
(A) 8
(B) 24
(C) 32
(D 56
(E) 80
NOTE: Let's call a brother-sister pair a FAMILY
Stage 1: Select 3 FAMILIES
Since the order in which we select the families does not matter, we can use COMBINATIONS
We can select 3 families from 4 families in 4C3 ways ( = 4 ways)
ASIDE: If anyone is interested, we have a video on calculating combinations (like 4C3) in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789
At this point, we have 3 FAMILIES, which we'll call A, B and C. We're now going to select ONE person from each family to be on the committee.
Stage 2: Select 1 person from family A
There are 2 people in this family, so we can complete this stage in 2 ways.
Stage 3: Select 1 person from family B
There are 2 people in this family, so we can complete this stage in 2 ways.
Stage 4: Select 1 person from family C
There are 2 people in this family, so we can complete this stage 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 ([spoiler]= 32 ways[/spoiler])
Answer: C
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Note: the FCP can be used to solve the majority of counting questions on the GMAT. For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat-counting?id=775
Then you can try solving the following questions:
EASY
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MEDIUM
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DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
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Cheers,
Brent
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Here's a similar question to practice with: https://www.beatthegmat.com/if-a-committ ... 92338.html