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If a committee of 3 people is to be selected from among 5 ma
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03 Sep 2020, 10:42
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65% (01:53) correct
35% (01:49) wrong based on 40 sessions
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If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?
Re: If a committee of 3 people is to be selected from among 5 ma
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03 Sep 2020, 11:31
1
Carcass wrote:
If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?
A. 20 B. 40 C. 50 D. 80 E. 120
Take the task of creating a committee and break it into stages.
Stage 1: Select 3 COUPLES Since the order in which we select the couples does not matter, we can use COMBINATIONS We can select 3 couples from 5 couples in 5C3 ways ( = 10 ways)
ASIDE: If anyone is interested, we have a video on calculating combinations (like 5C3) in your head (see bottom of post)
At this point, we have selected 3 COUPLES, which we'll call A, B and C. We're now going to select ONE person from each couple to be on the committee.
Stage 2: Select 1 person from couple A There are 2 people in this couple, so we can complete this stage in 2 ways.
Stage 3: Select 1 person from couple B There are 2 people in this couple, so we can complete this stage in 2 ways.
Stage 4: Select 1 person from couple C There are 2 people in this couple, 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 (10)(2)(2)(2) ways (= 80ways)
Answer: D
Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.
Re: If a committee of 3 people is to be selected from among 5 ma
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04 Sep 2020, 21:21
Carcass wrote:
If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?
A. 20 B. 40 C. 50 D. 80 E. 120
Using a more indirect method, you can subtract out the undesirable outcomes from the total number of outcomes to get the desired outcomes.
In this case, the undesired outcome is having a married couple out of the three spots in the committee.
There are a total of 10 people to choose from (5 couples). Order doesn't matter (A group of Person 1, Person 2, and Person 3 is the same group as Person 2, Person 1, and Person 3), so we use combinations.
10 Choose 3 = 10∗9∗83∗2=5∗3∗8=120
So if there were no restrictions, the total number of outcomes would be 120 different committees.
Now consider the undesired outcomes: choosing a married couple for 2 of the 3 spots on the committee.
Since there are 5 couples, if we choose 1 couple (2 people) to fill two spots, we could choose any of the remaining 8 people to fill the third spot. That's 8 different combinations for each of the 5 couples. So there are 40 different committees that include a married couple.
The total number of undesired outcomes then is 40.
Now we subtract: 120-40 = 80, giving us our answer of D.
Re: If a committee of 3 people is to be selected from among 5 ma
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24 Oct 2021, 22:00
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Re: If a committee of 3 people is to be selected from among 5 ma [#permalink]
03 Sep 2020, 10:42 
65% (01:53) correct
