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Sherry supervises a crew of maintenance engineers for an off
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sandy
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Joined: 07 Jun 2014
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GRE 1: Q167 V156
WE:Business Development (Energy and Utilities)
Sherry supervises a crew of maintenance engineers for an off [#permalink] New post  Updated on: 17 Jun 2020, 08:53
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Sherry supervises a crew of maintenance engineers for an office building. If there are 5 experienced maintenance engineers and 3 apprentice engineers and the engineers are sent out on jobs in teams, which of the following must be true?

Indicate all possible values.

A. There are 10 different 3-person teams of experienced engineers she could send.
B. There are 3 different 2-person teams of apprentice engineers she could send.
C. There are 2 different 2-person teams of apprentice engineers she could send.
D. There are 10 different 2-person teams of experienced engineers she could send.
E. There are 10 different 4-person teams of experienced engineers she could send.

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Originally posted by sandy on 30 Dec 2017, 14:11.
Last edited by Carcass on 17 Jun 2020, 08:53, edited 1 time in total.
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sandy
Retired Moderator
Joined: 07 Jun 2014
Posts: 4805
GRE 1: Q167 V156
WE:Business Development (Energy and Utilities)
Re: Sherry supervises a crew of maintenance engineers for an off [#permalink] New post  12 Jan 2018, 15:33
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Explanation

Starting with choice (A), there are 3 slots on the team, with 5 experienced engineers available for the first slot, 4 for the second slot, and 3 for the third slot. Order doesn’t matter, so divide by 3! to get \(\frac{5 \times 4 \times 3}{3 \times 2 \times 1}= 10\). Choice (A) is correct.

For choice (B), you have 3 apprentice engineers available for 2 slots and once again, order doesn’t matter. \(\frac{3 \times 2}{2 \times 1}= 3\). Choice (B) is correct and you can eliminate choice (C), which contradicts choice (B).


For choice (D) you have \(\frac{5 \times 4}{1 \times 2}= 10\), so choice (D) is correct.

Choice (E) is incorrect because \(\frac{5 \times 4 \times 3 \times 2}{4 \times 3 \times 2 \times 1}= 5\). The correct answers are choices (A), (B), and (D).
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Asmakan
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Re: Sherry supervises a crew of maintenance engineers for an off [#permalink] New post  17 Jun 2020, 05:49
I have a mini question here:
in B, when we do the math we get three after applying combination formula.
In C, the answer is also 3, which is less than two. So, having two different teams is embedded in 3 ? Could we think that or it is totally wrong?
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Carcass
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Re: Sherry supervises a crew of maintenance engineers for an off [#permalink] New post  17 Jun 2020, 08:57
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As Sandy at the time pointed out, C is false because you do have 3of 2 and NOT 2 of 2
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