A company will select 2 of the 6 candidates available to work in 2 different positions in Technology team and 3 of the 7

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Sun May 31, 2020 1:09 pm

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A company will select 2 of the 6 candidates available to work in 2 different positions in Technology team and 3 of the 7 candidates to work in the same position in HR team. Find the number of ways in which the company can fill the positions?

A. 57
B. 65
C. 128
D. 256
E. 1050

[spoiler]OA=E[/spoiler]

Source: e-GMAT

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Source: Beat The GMAT — Problem Solving | Sun May 31, 2020 1:09 pm

quichopipe: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Wed Apr 08, 2020 12:42 pm

Re: A company will select 2 of the 6 candidates available to work in 2 different positions in Technology team and 3 of t

by quichopipe » Wed Jun 03, 2020 2:36 pm

Let's fill the 2 positions in the technology team:
We need to select 2 candidates from 6 candidates but both of them will have different positions so we must use permutation in this case
6P2 = 30

Now, let's fill the 3 positions in the HR team
We need to select 3 candidates from 7 candidates but all of them will have identical positions so we must use combinations in this case
7C3 = 35

Combining both cases: 30*35 = 1050

Answer choice E.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8175; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: A company will select 2 of the 6 candidates available to work in 2 different positions in Technology team and 3 of t

by Scott@TargetTestPrep » Sat Apr 03, 2021 10:30 am

Gmat_mission wrote: ↑
Sun May 31, 2020 1:09 pm
A company will select 2 of the 6 candidates available to work in 2 different positions in Technology team and 3 of the 7 candidates to work in the same position in HR team. Find the number of ways in which the company can fill the positions?

A. 57
B. 65
C. 128
D. 256
E. 1050

[spoiler]OA=E[/spoiler]

Solution:

Since the positions in the Technology team are different (i.e., order matters), the number of ways to select the candidates for the two positions is 6P2 = 6 x 5 = 30.

Since the positions in the HR team are the same (i.e., order doesn’t matter), the number of ways to select the candidates for the three positions is 7C3 = (7 x 6 x 5)/(3 x 2) = 35.

Therefore, there are 30 x 35 = 1050 ways to select the candidates for the positions.

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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