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Combinatorics problem - Please help experts
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20 Dec 2021, 03:25
20 Dec 2021, 03:25
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Question Stats:
66% (01:12) correct
33% (02:12) wrong based on 12 sessions
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10 lawmakers are being considered to participate in a special committee. Of these, 5 lawmakers will be selected, 4 of which will be committee members, and 1 will be committee chairperson. How many possible special committees can be made?
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1260
Re: Combinatorics problem - Please help experts
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20 Dec 2021, 04:01
20 Dec 2021, 04:01
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Please provide the OA
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Re: Combinatorics problem - Please help experts
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20 Dec 2021, 06:36
20 Dec 2021, 06:36
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darkshadow271 wrote:
10 lawmakers are being considered to participate in a special committee. Of these, 5 lawmakers will be selected, 4 of which will be committee members, and 1 will be committee chairperson. How many possible special committees can be made?
Show: ::
1260
Take the task of creating the special committee, and break it into stages.
Stage 1: Select 1 person to be the committee chairperson
There are 10 lawmakers from which to choose. So, we can complete stage 1 in 10 ways
Stage 2: Select 4 people to serve as committee members
Since the order in which we select the committee members does not matter, we can use combinations.
We can select 4 people from the 9 remaining lawmakers in 9C4 ways (= (9)(8)(7)(6)/(4)(3)(2)(1) = 126 ways)
So, we can complete stage 2 in 126 ways
By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create the special committee) in (10)(126) ways (= 1260 ways)
Answer: 1260
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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