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GMATGuruNY
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Number of options for the 1st person = 8.A committee of three people is to be chosen from four married couples. What is the number of different commities that can be chosen if two people who are married to each other cannot both serve on this committee?
16
24
26
30
32
Number of options for the 2nd person = 6. (Of the 7 remaining people, anyone but the spouse of the first person selected.)
Number of options for the 3rd person = 4. (Of the 6 remaining people, anyone but the spouses of the first 2 people selected.)
To combine these options, we multiply:
8*6*4.
Since the ORDER of the selections doesn't matter -- ABC is the same committee as BCA -- the product above must be divided by the number of ways to ARRANGE the 3 people chosen (3!):
(8*6*4)/(3*2*1) = 32.
The correct answer is E.
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GMATGuruNY
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Check my SECOND post here:macattack wrote:Thanks that was really helpful. However i would like to know how you got the 3!. What is the mathematical rule behind it. THanks.
https://www.beatthegmat.com/counting-problem-t72690.html
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Brent@GMATPrepNow
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Here's another approach:A committee of three people is to be chosen from four married couples. What is the number of different committee that can be chosen if two people who are married to each other cannot both serve on the committee?
A. 16
B. 24
C. 26
D. 30
E. 32
Take the task of selecting the 3 committee members and break it into stages.
Stage 1: Select the 3 couples from which we will select 1 spouse each.
There are 4 couples, and we must select 3 of them. Since the order in which we select the 3 couples does not matter, this stage can be accomplished in 4C3 ways (4 ways)
If anyone is interested, we have a free video on calculating combinations (like 4C3) in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789
Stage 2: Take one of the 3 selected couples and choose 1 person to be on the committee.
There are 2 people in the couple, so this stage can be accomplished in 2 ways.
Stage 3: Take one of the 3 selected couples and choose 1 person to be on the committee.
There are 2 people in the couple, so this stage can be accomplished in 2 ways.
Stage 4: Take one of the 3 selected couples and choose 1 person to be on the committee.
There are 2 people in the couple, 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 = E
Cheers,
Brent
Aside: For more information about the FCP, we have a free video on the subject: https://www.gmatprepnow.com/module/gmat-counting?id=775
Brent Hanneson - Creator of GMATPrepNow.com
