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Alice and David are two of the ten people in a group. In how
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14 Jul 2019, 15:36
14 Jul 2019, 15:36
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Alice and David are two of the ten people in a group. In how many different ways can this group of 10 people be divided into a group of 7 people and a group of 3 people if Alice and David are to be in the same group?
A. 48
B. 56
C. 64
D. 80
E. 128
A. 48
B. 56
C. 64
D. 80
E. 128
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Concentration: General Management
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GMAT 1: 700 Q51 V31
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Re: Alice and David are two of the ten people in a group. In how
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07 Jun 2020, 03:09
07 Jun 2020, 03:09
There are two possibilities
Case 1: Alice and David are tine group of 7 people
So we need to pick remaining 5 people in that group from 8 people (10-2 (Alice and David) )
5 people can be picked from 8 people in 8C5 ways
= \(\frac{8!}{(5!*3!)}\) = \(\frac{8*7*6*5!}{(5!*3!)}\)
= \(\frac{8*7*6}{3*2*1}\) = 56 ways
Remaining people will go in group of 3 so we do not need to calculate their possibilities
Case 2: Alice and David are tine group of 3 people
So we need to pick remaining 1 person in that group from 8 people (10-2 (Alice and David) )
1 person can be picked from 8 people in 8C1 ways
= \(\frac{8!}{(7!*1!)}\) = \(\frac{8*7!}{(7!*1)}\)
= 8 ways
Remaining people will go in group of 7 so we do not need to calculate their possibilities
So, total number of ways = 56 + 8 = 64
So, answer will be C
Hope it helps!
Case 1: Alice and David are tine group of 7 people
So we need to pick remaining 5 people in that group from 8 people (10-2 (Alice and David) )
5 people can be picked from 8 people in 8C5 ways
= \(\frac{8!}{(5!*3!)}\) = \(\frac{8*7*6*5!}{(5!*3!)}\)
= \(\frac{8*7*6}{3*2*1}\) = 56 ways
Remaining people will go in group of 3 so we do not need to calculate their possibilities
Case 2: Alice and David are tine group of 3 people
So we need to pick remaining 1 person in that group from 8 people (10-2 (Alice and David) )
1 person can be picked from 8 people in 8C1 ways
= \(\frac{8!}{(7!*1!)}\) = \(\frac{8*7!}{(7!*1)}\)
= 8 ways
Remaining people will go in group of 7 so we do not need to calculate their possibilities
So, total number of ways = 56 + 8 = 64
So, answer will be C
Hope it helps!
Re: Alice and David are two of the ten people in a group. In how
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24 Oct 2021, 21:31
24 Oct 2021, 21:31
Hello from the GRE Prep Club BumpBot!
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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.
