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Combination

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Intern
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Combination [#permalink] New post 22 Jun 2017, 05:49
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Question Stats:

100% (01:11) correct 0% (00:00) wrong based on 3 sessions
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?

[Reveal] Spoiler:
700
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Re: Combination [#permalink] New post 22 Jun 2017, 07:18
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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 [#permalink] New post 27 Jun 2017, 11:54
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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:
[Reveal] Spoiler:
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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Re: Combination [#permalink] New post 28 Sep 2018, 21:10
Why we multiplied 35 and 20. Till here I solved correctly but after that I added both these numbers.. Please explain me the last step.
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Re: Combination [#permalink] New post 29 Sep 2018, 11:55
Expert's post
Reetika1990 wrote:
Why we multiplied 35 and 20. Till here I solved correctly but after that I added both these numbers.. Please explain me the last step.


It is a Fundamental Counting Principle .

Please review you math.

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Re: Combination   [#permalink] 29 Sep 2018, 11:55
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