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# A city council will select 2 of 9 available firefighters and

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Senior Manager
Affiliations: UWC
Joined: 09 May 2012
Posts: 393

Kudos [?]: 1676 [5], given: 100

GMAT 1: 620 Q42 V33
GMAT 2: 680 Q44 V38
GPA: 3.43
WE: Engineering (Entertainment and Sports)
A city council will select 2 of 9 available firefighters and [#permalink]

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27 May 2012, 08:08
5
KUDOS
00:00

Difficulty:

5% (low)

Question Stats:

80% (00:37) correct 20% (00:41) wrong based on 123 sessions

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A city council will select 2 of 9 available firefighters and 1 of 6 available police officers to serve on an advisory panel. How many different groups of 3 could serve on the panel?

A. 36
B. 72
C. 144
D. 216
E. 432
[Reveal] Spoiler: OA

Kudos [?]: 1676 [5], given: 100

Intern
Joined: 01 Apr 2012
Posts: 26

Kudos [?]: 14 [0], given: 18

Location: United States
Concentration: Technology, Economics
GMAT Date: 05-13-2012
WE: Consulting (Computer Software)
Re: A city council will select 2 of 9 available firefighters a [#permalink]

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27 May 2012, 22:39
OA D

9C2 * 6C1

using the combination formula to choose 2 from 9 and 1 from 6

Kudos [?]: 14 [0], given: 18

Math Expert
Joined: 02 Sep 2009
Posts: 42578

Kudos [?]: 135467 [3], given: 12695

Re: A city council will select 2 of 9 available firefighters and [#permalink]

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28 May 2012, 01:04
3
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Expert's post
macjas wrote:
A city council will select 2 of 9 available firefighters and 1 of 6 available police officers to serve on an advisory panel. How many different groups of 3 could serve on the panel?

A. 36
B. 72
C. 144
D. 216
E. 432

Ways to select 2 firefighters out of 9 is $$C^2_9=36$$;
Ways to select 1 police officer out of 6 is $$C^1_6=6$$;

Total ways to select 2 firefighters out of 9 and 1 police officer out of 6 is 36*6=216.

It's called Principle of Multiplication: if one event can occur in m ways and a second can occur independently of the first in n ways, then the two events can occur in m*n ways.

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Kudos [?]: 135467 [3], given: 12695

Manager
Joined: 26 Feb 2013
Posts: 170

Kudos [?]: 53 [0], given: 25

Re: A city council will select 2 of 9 available firefighters and [#permalink]

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07 Sep 2013, 23:09
The "how many different groups of 3" threw me at first, I thought I needed to exclude something, or say something like "we got 15 in total, so 5 groups of 3..." and so some calculations there.

Can someone please explain to me, in which case we would have divided the product of the two combinations by the total people selected out of the population? i.e. 15C5

Kudos [?]: 53 [0], given: 25

Math Expert
Joined: 02 Sep 2009
Posts: 42578

Kudos [?]: 135467 [0], given: 12695

Re: A city council will select 2 of 9 available firefighters and [#permalink]

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08 Sep 2013, 04:00
Skag55 wrote:
The "how many different groups of 3" threw me at first, I thought I needed to exclude something, or say something like "we got 15 in total, so 5 groups of 3..." and so some calculations there.

Can someone please explain to me, in which case we would have divided the product of the two combinations by the total people selected out of the population? i.e. 15C5

We would divide by 15C3 if the question were: what is the probability that when we select 3 people out of 9 firefighters and 6 police officers we get 2 firefighters and 1 police officer.
_________________

Kudos [?]: 135467 [0], given: 12695

Manager
Joined: 26 Feb 2013
Posts: 170

Kudos [?]: 53 [0], given: 25

Re: A city council will select 2 of 9 available firefighters and [#permalink]

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08 Sep 2013, 09:30
Great, many thanks!

Kudos [?]: 53 [0], given: 25

Re: A city council will select 2 of 9 available firefighters and   [#permalink] 08 Sep 2013, 09:30
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