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An engagement team consists of a project manager, team leader, and

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An engagement team consists of a project manager, team leader, and [#permalink]

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An engagement team consists of a project manager, team leader, and four consultants. There are 2 candidates for the position of project manager, 3 candidates for the position of team leader, and 7 candidates for the 4 consultant slots. If 2 of the 7 consultants refuse to be on the same team, how many different teams are possible?

A. 25
B. 35
C. 150
D. 210
E. 300
[Reveal] Spoiler: OA

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An engagement team consists of a project manager, team leader, and [#permalink]

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New post 06 Jun 2017, 12:34
Project manager - 2
Team leader - 3
Four consultants - 7

Total number of combinations = 2\(C_1\) * 3\(C_1\) * 7\(C_4\) = 2*3*35 = 210


Total number of combinations when both consultants are together = 2\(C_1\) * 3\(C_1\) * 5\(C_2\) = 2*3*10=60

Number of Teams possible = 210-60 = 150

Answer is C

Last edited by quantumliner on 13 Jun 2017, 16:09, edited 1 time in total.

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Re: An engagement team consists of a project manager, team leader, and [#permalink]

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New post 13 Jun 2017, 14:58
Quote:
Total number of combinations when both consultants are together


Should total up to 60 vice 40.
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Re: An engagement team consists of a project manager, team leader, and [#permalink]

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New post 13 Jun 2017, 16:48
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The number of ways to choose the project manager is 2 and the number of ways to choose a team leader is 3.
The total number of ways to choose 4 consultants out of 7 candidates is 7!/(4!3)= 35, however, we must also take into the consideration that 2 candidates refuse to work together and for that reason, we must deduct from the total number of ways all the options when these 2 are together. We do it by counting all the outcomes, when these 2 are already in team and there are still 2 spots available: 5!/(2!*3!) = 10, so there are 35-10=25 ways of picking 4 candidates out of 7, taking into the consideration the fact that 2 of them don't want to work together. The only thing that remains now is to multiply all outcomes 2*3*25=150
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Re: An engagement team consists of a project manager, team leader, and [#permalink]

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New post 02 Aug 2017, 13:25
quantumliner wrote:
Project manager - 2
Team leader - 3
Four consultants - 7

Total number of combinations = 2\(C_1\) * 3\(C_1\) * 7\(C_4\) = 2*3*35 = 210


Total number of combinations when both consultants are together = 2\(C_1\) * 3\(C_1\) * 5\(C_2\) = 2*3*10=60

Number of Teams possible = 210-60 = 150

Answer is C


How do we get 5C2 when we calculate the total number of combinations when consultants are together?

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Re: An engagement team consists of a project manager, team leader, and [#permalink]

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New post 03 Aug 2017, 06:08
TheMastermind wrote:
How do we get 5C2 when we calculate the total number of combinations when consultants are together?


Hi TheMastermind ,

When I am saying two consultants are always together, that means I already have them on my bucket and now I have to select the pending 2 from the remaining 5 consultants. Thus, we are using 5C2

Let me know if you need the detailed explanation for this question. :)
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Re: An engagement team consists of a project manager, team leader, and   [#permalink] 03 Aug 2017, 06:08
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