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A research team is to consist of 3 scientists from Company A
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29 Jul 2020, 11:04
29 Jul 2020, 11:04
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A research team is to consist of 3 scientists from Company A and 3 scientists from Company B. If the pool of available scientists from Company A is 5 and the pool of available scientists from Company B is 4 scientists, how many different research teams are possible?
(A) 84
(B) 40
(C) 30
(D) 20
(E) 12
Kudos for the right answer and explanation
(A) 84
(B) 40
(C) 30
(D) 20
(E) 12
Kudos for the right answer and explanation
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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: A research team is to consist of 3 scientists from Company A
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29 Jul 2020, 11:16
29 Jul 2020, 11:16
Carcass wrote:
A research team is to consist of 3 scientists from Company A and 3 scientists from Company B. If the pool of available scientists from Company A is 5 and the pool of available scientists from Company B is 4 scientists, how many different research teams are possible?
(A) 84
(B) 40
(C) 30
(D) 20
(E) 12
Kudos for the right answer and explanation
(A) 84
(B) 40
(C) 30
(D) 20
(E) 12
Kudos for the right answer and explanation
Take the task of seating the 6 scientists and break it into stages.
Stage 1: Select 3 scientists from Company A
Since the order in which we select the scientists does not matter, we can use combinations.
We can select 3 scientists from the 5 scientists in pool Company A in 5C3 ways (10 ways)
So, we can complete stage 1 in 10 ways
Stage 2: Select 3 scientists from Company B
Once again, we can use combinations.
We can select 3 scientists from the 5 scientists in pool Company B in 4C3 ways (4 ways)
So, we can complete stage 2 in 4 ways
By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus curate the research team) in (10)(4) ways (= 40 ways)
Answer: B
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: A research team is to consist of 3 scientists from Company A [#permalink]
29 Jul 2020, 11:16
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