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Combination
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22 Jun 2017, 05:49
22 Jun 2017, 05:49
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Question Stats:
85% (01:02) correct
14% (01:01) wrong based on 35 sessions
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Three men (out of 7) and 3 women (out of 6) will be chosen to serve on a committee. In how many ways can the committee be formed?
Show: ::
700
Re: Combination
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22 Jun 2017, 07:18
22 Jun 2017, 07:18
1
Vrushali wrote:
Three men (out of 7) and 3 women (out of 6) will be chosen to serve on a committee. In how many ways can the committee be formed?
to select 3 Men out of 7 men will be done in= 7c3 ways = 35ways
to select 3 women out of 6 women will be done in = 6c3 ways =20ways
Total number of ways = 35x20 = 700 ways
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Re: Combination
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27 Jun 2017, 11:54
27 Jun 2017, 11:54
1
Vrushali wrote:
Three men (out of 7) and 3 women (out of 6) will be chosen to serve on a committee. In how many ways can the committee be formed?
Take the task of seating the 6 people and break it into stages.
Stage 1: Select 3 men to be on the committee
Since the order in which we select the men does not matter, we can use combinations.
We can select 3 men from 7 men in 7C3 ways (35 ways)
So, we can complete stage 1 in 35 ways
Stage 2: Select 3 women to be on the committee
Since the order in which we select the women does not matter, we can use combinations.
We can select 3 women from 6 women in 6C3 ways (20 ways)
So, we can complete stage 2 in 20 ways
By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create a 6-person committee) in (35)(20) ways (= 700 ways)
Answer:
Show: ::
700
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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