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# A jazz ensemble is holding auditions for new musicians.

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Manager
Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 184
A jazz ensemble is holding auditions for new musicians.  [#permalink]

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25 Mar 2019, 12:41
00:00

Difficulty:

15% (low)

Question Stats:

85% (01:57) correct 15% (02:44) wrong based on 20 sessions

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A jazz ensemble is holding auditions for new musicians. 11 total musicians are auditioning, and 6 total will be chosen for the ensemble. If 7 of the musicians are saxophone players and 4 of the musicians are clarinet players, how many different groups of 4 saxophone players and 2 clarinet players can be selected?

A) 66
B) 192
C) 210
D) 420
E) 462
Intern
Joined: 25 Jun 2017
Posts: 29
GMAT 1: 660 Q45 V36
GPA: 3.5
WE: Human Resources (Consumer Products)
Re: A jazz ensemble is holding auditions for new musicians.  [#permalink]

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25 Mar 2019, 14:33
energetics wrote:
A jazz ensemble is holding auditions for new musicians. 11 total musicians are auditioning, and 6 total will be chosen for the ensemble. If 7 of the musicians are saxophone players and 4 of the musicians are clarinet players, how many different groups of 4 saxophone players and 2 clarinet players can be selected?

A) 66
B) 192
C) 210
D) 420
E) 462

Out of 7 sax players, we choose 4. Out of 4 clarinet players, we choose 2. We multiply the two events as these two events can happen simultaneously.

Therefore, 7C4*4C2

=$$\frac{7!}{4!3!}$$ *$$\frac{4!}{2!2!}$$

= 210
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Re: A jazz ensemble is holding auditions for new musicians.   [#permalink] 25 Mar 2019, 14:33
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