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# A four-person leadership committee is to be chosen from a

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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1782 [0], given: 397

A four-person leadership committee is to be chosen from a [#permalink]  30 Dec 2017, 13:18
Expert's post
00:00

Question Stats:

95% (00:39) correct 5% (01:53) wrong based on 20 sessions
A four-person leadership committee is to be chosen from a student council that consists of seven juniors and five seniors. Q is the total number of different leadership committees that include three seniors and one junior.

 Quantity A Quantity B Q 75

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.

Drill 1
Question: 11
Page: 561
[Reveal] Spoiler: OA
GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1782 [0], given: 397

Re: A four-person leadership committee is to be chosen from a [#permalink]  07 Jan 2018, 18:24
Expert's post
Explanation

Start by finding out how many groups of three seniors can be chosen from the five seniors: $$\frac{5}{3} \times \frac{4}{2} \times \frac{3}{1}=10$$.

Next, multiply that total by the number of individual juniors with which those groups can be paired (7) to form the full committee: 10 × 7 = 70. Quantity B is greater.
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Sandy
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Intern
Joined: 20 Dec 2017
Posts: 30
Followers: 0

Kudos [?]: 17 [0], given: 9

Re: A four-person leadership committee is to be chosen from a [#permalink]  07 Jan 2018, 23:29
J=7
S=5

Since we need 3J and 1S, 5C3 = 5*4*3!/2!3!=10 and 7C1=7, hence 7*10=70.
Therefore B is greater
Re: A four-person leadership committee is to be chosen from a   [#permalink] 07 Jan 2018, 23:29
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