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# What is the difference between the number of three-member co

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What is the difference between the number of three-member co [#permalink]  30 Dec 2017, 13:34
Expert's post
00:00

Question Stats:

94% (01:18) correct 5% (02:09) wrong based on 19 sessions
What is the difference between the number of three-member committees that can be formed from a group of nine members and the total number of ways there are to arrange the members
of such a committee?

A. 0
B. 84
C. 252
D. 420
E. 504

Drill 1
Question: 9
Page: 560-561
[Reveal] Spoiler: OA

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Sandy
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Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 171

Kudos [?]: 2915 [0], given: 394

Re: What is the difference between the number of three-member co [#permalink]  07 Jan 2018, 18:20
Expert's post
Explanation

To find the number of different committees. Make your slots and divide by the factoral $$\frac{9}{3}\frac{8}{2}\frac{7}{1}$$=84; eliminate choice (B).

To find the number of ways to arrange the committee members, just multiply 9 × 8 × 7 = 504, and eliminate partial choice (E). The difference is 504 − 84 = 420, choice D.
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Sandy
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Re: What is the difference between the number of three-member co [#permalink]  08 Jan 2018, 02:42
understood the solution. I got 84- 3! ( wording of the question made it a bit difficult)
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Target Test Prep Representative
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Re: What is the difference between the number of three-member co [#permalink]  05 Jun 2018, 09:10
Expert's post
sandy wrote:
What is the difference between the number of three-member committees that can be formed from a group of nine members and the total number of ways there are to arrange the members
of such a committee?

A. 0
B. 84
C. 252
D. 420
E. 504

The number of 3-member committees that can be formed from 9 people (i.e., order doesn’t matter) is 9C3 = 9!/(3! x 6!) = (9 x 8 x 7)/3! = (9 x 8 x 7)/(3 x 2) = 3 x 4 x 7 = 84.

The number of ways to form the committees and arrange the members (i.e., order matters) is 9P3 = 9 x 8 x 7 = 504.

Thus, the difference is 504 - 84 = 420.

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# Jeffrey Miller

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Re: What is the difference between the number of three-member co [#permalink]  17 Jun 2020, 01:20
Not an OG Big book question
Re: What is the difference between the number of three-member co   [#permalink] 17 Jun 2020, 01:20
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