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A city council will select 2 of 9 available firefighters and

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A city council will select 2 of 9 available firefighters and [#permalink] New post 27 May 2012, 08:08
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Question Stats:

83% (01:39) correct 17% (00:47) wrong based on 92 sessions
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
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Re: A city council will select 2 of 9 available firefighters a [#permalink] New post 27 May 2012, 22:39
OA D

9C2 * 6C1

using the combination formula to choose 2 from 9 and 1 from 6
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Re: A city council will select 2 of 9 available firefighters and [#permalink] New post 28 May 2012, 01:04
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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.

Answer: D.
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Re: A city council will select 2 of 9 available firefighters and [#permalink] New post 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
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Re: A city council will select 2 of 9 available firefighters and [#permalink] New post 08 Sep 2013, 04:00
Expert's post
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.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: A city council will select 2 of 9 available firefighters and [#permalink] New post 08 Sep 2013, 09:30
Great, many thanks!
Re: A city council will select 2 of 9 available firefighters and   [#permalink] 08 Sep 2013, 09:30
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