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# Of a group of 10 PTA members, a committee will be selected t

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GRE Prep Club Legend
Joined: 07 Jun 2014
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GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1783 [0], given: 397

Of a group of 10 PTA members, a committee will be selected t [#permalink]  30 Dec 2017, 14:25
Expert's post
00:00

Question Stats:

85% (00:24) correct 14% (03:46) wrong based on 7 sessions
Of a group of 10 PTA members, a committee will be selected that has 1 president and 3 other members. How many different committees could be selected?

Drill 2
Question: 4
Page: 563

[Reveal] Spoiler: OA
840

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Sandy
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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1783 [0], given: 397

Re: Of a group of 10 PTA members, a committee will be selected t [#permalink]  08 Jan 2018, 16:27
Expert's post
Explanation

There are 10 possible presidents.

After the president is selected, there are 9 members left to fill the remaining 3 spots. Order does not matter, so the number of possibilities for the other three spots is $$\frac{9 \times 8 \times 7}{3 \times 2 \times 1}$$ . Simplifying the fraction yields 3 × 4 × 7 = 84.

So, there are 10 possible presidents and 84 possible committees for each president. Multiplying them yields the total number of possible committees, 840.
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Sandy
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Kudos [?]: 1475 [1] , given: 8

Re: Of a group of 10 PTA members, a committee will be selected t [#permalink]  29 Jan 2018, 17:40
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Expert's post
sandy wrote:
Of a group of 10 PTA members, a committee will be selected that has 1 president and 3 other members. How many different committees could be selected?

Take the task of creating the committee and break it into stages.

Stage 1: Select a person to be president.
We can choose any of the 10 PTA members, so we can complete stage 1 in 10 ways

Stage 2: Select the 3 other members
Since the order in which we select the 3 other members does not matter, we can use combinations.
We can select 3 people from the remaining 9 people in 9C3 ways (84 ways)
So, we can complete stage 2 in 84 ways

By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create the 4-person committee) in (10)(84) ways (= 840 ways)

Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.

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Re: Of a group of 10 PTA members, a committee will be selected t   [#permalink] 29 Jan 2018, 17:40
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