An engagement team consists of a project manager, team leader, and four consultants. There are 2 candidates for the

Question

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

OA C

Source: Veritas Prep

Brent@GMATPrepNow · Answer

BTGmoderatorDC wrote: ↑Sun Dec 06, 2020 4:57 pm 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 OA C Source: Veritas Prep For this question, let's first ignore the restriction regarding the two consultants who refuse to work together and find the total number of different teams. Then we'll determine how many of those teams break the rule about the two consultants. In other words, # of "good" teams = Total number of teams (ignoring the restriction) - # of "bad" teams (that break the rule) Total number of teams (ignoring the restriction) Take the task of building teams and break it into stages. Stage 1: Select a project manager There are 2 candidates for this position, so we can complete stage 1 in 2 ways Stage 2: Select a team leader There are 3 candidates for this position, so we can complete stage 2 in 3 ways Stage 3: Select the four consultants Since the order in which we select the consultants does not matter, we can use combinations. We can select 4 consultants from 7 consultants in 7C4 ways (35 ways) If anyone is interested, we have a video on calculating combinations (like 7C4) in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789 By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus build our team) in (2)(3)(35) ways ( = 210 ways) # of "bad" teams (that break the rule) Take the task of building "bad" teams and break it into stages. Stage 1: Select a project manager There are 2 candidates for this position, so we can complete stage 1 in 2 ways Stage 2: Select a team leader There are 3 candidates for this position, so we can complete stage 2 in 3 ways Stage 3: Select four consultants Here, we want to break the rule. So, let's place the two bickering consultants on the team. So, for this stage, we need only select two other consultants to join them. Since the order in which we select the 2 remaining consultants does not matter, we can use combinations. We can select 2 consultants from the remaining 5 consultants in 5C2 ways (10 ways) By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus build our "bad" team) in (2)(3)(10) ways ( = 60 ways) So, # of "good" teams = 210 - 60 = 150 = C Cheers, Brent

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