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An engagement team consists of a project manager, team leade

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Joined: 28 May 2017
Posts: 6
GMAT 1: 640 Q44 V34
Re: An engagement team consists of a project manager, team leade [#permalink]

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New post 30 Aug 2017, 02:35
A very easy approach :
Total ways without the constraints = 2C1 x 3C1 x 7C4 = 2 * 3 * 7C4 = 6 * 7C4 = 210.
Now we know that the answer is less than 210 and a multiple of 6. So answer = C.
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Re: An engagement team consists of a project manager, team leade [#permalink]

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New post 02 Sep 2017, 06:10
marcodonzelli wrote:
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 out of 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


We can select the project manager in 2 ways and the team leader in 3 ways. For the consultants, there are 7 candidates for 4 positions, but 2 of the 7 cannot be together.

We can use the following equation:

# of ways to select the consultants = # of ways with the 2 together + # of ways with the 2 not together.

The total number of ways to select the consultants is 7C4 = 7!/[4!(7-4)!] = 7!/(4!3!) = (7 x 6 x 5 x 4)/4! = 7 x 6 x 5 x 4)/(4 x 3 x 2) = 35.

The number of ways to select the consultants when the 2 are together can be found by choosing 2 people for the remaining slots from the 5 remaining candidates, which is given by 5C2 = (5 x 4)/2 = 10.

Thus, the number of ways to select the consultants when the 2 are not together is 35 - 10 = 25.

So, the total number of ways to select the teams is 2 x 3 x 25 = 150.

Answer: C
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Re: An engagement team consists of a project manager, team leade   [#permalink] 02 Sep 2017, 06:10

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