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An engagement team consists of a project manager, team leade

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Posts: 221
Re: An engagement team consists of a project manager, team leade [#permalink]

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New post 20 Jun 2018, 10:27
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


Given a team is to be formed of 1 PM, 1 TL & 4 consultants, out of 2 candidates for the position of PM, 3 candidates for TL & 7 for consultants.

Constraint is that 2 of the 7 consultants cannot be on same team. Let these 2 be called A & B

We have two cases:

Case 1: Choose one of the 2 consultants ( A or B) & put him on the team & choose the rest 3 from the remaining 5.

We get # of ways as = 2C1 * 5C3 * 2C1 * 3C1 = 2 * (5*4*3/1*2*3) * 2 *3 = 120

Case 2: Exclude both A & B and choose the 4 consultants from the remaining 5 consultants.

We get # of ways as = 5C4 * 2C1 * 3C1 = 5 * 2 * 3 = 30

Hence total # of ways = 120 + 30 = 150

Answer C.


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GyM
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Re: An engagement team consists of a project manager, team leade [#permalink]

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New post 20 Jun 2018, 11:14
2 * 3 * Ways of choosing 4 Consultants
Consultant candidates: a b c d e f g
a b not on the same team

either a/b on the team
2 * 1 * 5C3 = 20

neither a b on the team
5C4 = 5

So 25 ways for choosing 4 consultants

2 * 3 * 25 = 150
Answer C
Re: An engagement team consists of a project manager, team leade   [#permalink] 20 Jun 2018, 11:14

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