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A city council will select 2 of 9 available firefighters and

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by BTGmoderatorDC » Wed Dec 12, 2018 10:20 pm
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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

OA D

Source: Princeton Review
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by fskilnik@GMATH » Thu Dec 13, 2018 4:50 am
BTGmoderatorDC 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
Source: Princeton Review
$$? = C\left( {9,2} \right) \cdot 6 = \frac{{9 \cdot 8}}{2} \cdot 6 = \underleftrightarrow {3 \cdot 8 \cdot \left( {10 - 1} \right) = 240 - 24} = 216\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left( {\text{D}} \right)$$

This solution follows the notations and rationale taught in the GMATH method.

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by Scott@TargetTestPrep » Mon Mar 11, 2019 7:00 am
BTGmoderatorDC 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

OA D

Source: Princeton Review
The number of ways to select the firefighters is 9C2 = 9!/(2! x 7!) = (9 x 8)/2! = 36.

The number of ways to select the police officers is 6C1 = 6s.

The total number of ways to select the group is 36 x 6 = 216.

Answer: D

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by [email protected] » Mon Mar 11, 2019 11:26 am
Hi All,

We're told that a city council will select 2 of 9 available firefighters and 1 of 6 available police officers to serve on an advisory panel. We're asked for the number of different groups of 3 people that could serve on the panel. This question is essentially a Combination Formula question that requires a bit of extra Arithmetic.

To start, we can use the Combination Formula to determine the number of pairs of firefighters: 9c2 = 9!/2!(9-2)! = (9)(8)/(2)(1) = 36 possible pairs of firefighters.

With 6 possible police officers, we can 'pair' each officer with each of the 36 possible pairs of firefighters --> (6)(36) = 216 possible groups of 3 people.

Final Answer: D

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