A company will select 2 of the 6 candidates available to work in 2 dif

Solution

Given:

• A company will select 2of the 6 candidates available to work in 2 different positions in Technology team.
• And, the company will also select 3 of the 7 candidates to work in the same position in HR team.

To find:

• We need to find the number of ways in which company can fill all the positions.

Approach and Working:

• Total ways= Ways to fill 2 positions in technology team * Ways to fill 3 positions in HR team

Ways to fill 2 positions in technology team:

• We need to select 2 candidates from 6 candidates but both of them will have different positions.

o This is the case of arrangement of 2 people for two positions.
• Hence, total ways to fill 2 positions= \(^6P_2\)=30

Ways to fill 3 positions in HR team:

• We need to select 2 candidates from 6 candidates but all of them will have identical positions.

o This is the case of arrangement of identical objects.
• Hence, total ways to fill 3 positions= \(^7C_3\)=35

Thus, total ways to fill all the positions= 30*35= 1050.
Hence, the correct answer is option E.

Answer: E
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I'm getting a totally different answer...

Task 1 AND Task 2 = (select 2 out of 6 to work in 2 different positions) AND (select 3 out of 7 to work in the same position)

Task 1: since the positions are different, AB is different from BA, which makes this an arrangement question. 6P2=30.
30 ways to select 2 out of 6 to work in 2 different positions
or different way to think of it, there are 6 ways to fill the first tech position and 5 ways to fill the 2nd tech position. total = 30 ways to fill 2 diff tech positions

Task 2: since it's the same position, ABC is the same as CBA is the same as BAC etc, which makes this a selection question. 7C3=35
35 ways to select 3 out of 7 to work in the same position

Task 1 AND Task 2 = 30*35=1050

Where's my mistake?

[quote="aserghe1"]I'm getting a totally different answer...

Task 1 AND Task 2 = (select 2 out of 6 to work in 2 different positions) AND (select 3 out of 7 to work in the same position)

Task 1: since the positions are different, AB is different from BA, which makes this an arrangement question. 6P2=30.
30 ways to select 2 out of 6 to work in 2 different positions
or different way to think of it, there are 6 ways to fill the first tech position and 5 ways to fill the 2nd tech position. total = 30 ways to fill 2 diff tech positions

Task 2: since it's the same position, ABC is the same as CBA is the same as BAC etc, which makes this a selection question. 7C3=35
35 ways to select 3 out of 7 to work in the same position

Task 1 AND Task 2 = 30*35=1050 : these needs to be added as they are independent circumstances

Task 1 AND Task 2 = 30+35=65

Hey,


There is no mistake in your solution. 1050 is the correct answer.


Regards,
Saquib
Quant Expert
e-GMAT
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Hey Everyone,

Official solution to the question has been posted.

Regards,
Ashutosh
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Hi EgmatQuantExpert,

Could you please verify my approach?

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

Equation = {(Select 2 candidates out of 6) and (Select 1 position out of 2 different positions) (Select the remaining position) } and { (Select 3 candidate out of 7) and (Select 3 identical jobs out of 3 identical jobs)}
= {6C2 * 2C1 * 1C1 } AND { 7C3 * 1C1}
= 30 * 35 = 1050

Although, I got the answer I want to ask how did we take into account the assigning of each job to the candidates?
Thank you.

should just be [6C2*2!] * [7C3] or [6*5]*[7C3]. Either approach works.
6 choose 2 ways to pick, 2! ways to arrange. 7 choose 3 ways to pick. multiple the independent events together, and boom. Easy

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
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Hi,

Why are we multiplying 30*35 ? Aren't these 2 completely independent events ? We are selecting teams from 2 different pool of candidates...
please explain...
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