Last visit was: 14 Nov 2024, 09:36 It is currently 14 Nov 2024, 09:36

Close

GRE Prep Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GRE score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Verbal Expert
Joined: 18 Apr 2015
Posts: 29958
Own Kudos [?]: 36219 [2]
Given Kudos: 25903
Send PM
Verbal Expert
Joined: 18 Apr 2015
Posts: 29958
Own Kudos [?]: 36219 [0]
Given Kudos: 25903
Send PM
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12188 [0]
Given Kudos: 136
Send PM
Manager
Manager
Joined: 05 Aug 2020
Posts: 101
Own Kudos [?]: 244 [0]
Given Kudos: 14
Send PM
Re: If a committee of 3 people is to be selected from among 5 ma [#permalink]
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 = \(\frac{10*9*8}{3*2} = 5*3*8 = 120\)

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.
User avatar
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 5014
Own Kudos [?]: 74 [0]
Given Kudos: 0
Send PM
Re: If a committee of 3 people is to be selected from among 5 ma [#permalink]
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Prep Club for GRE Bot
Re: If a committee of 3 people is to be selected from among 5 ma [#permalink]
Moderators:
GRE Instructor
78 posts
GRE Forum Moderator
37 posts
Moderator
1111 posts
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne