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

Question

3 Deadly mistakes in Permutation and Combination - Exercise Question #3

3-  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 company can fill the positions?

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

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EgmatQuantExpert · Answer

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

aserghe1 · Answer

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?

GMAT215 · Answer

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

EgmatQuantExpert · Answer

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

Regards, Saquib Quant Expert e-GMAT

EgmatQuantExpert · Answer

Hey Everyone,

Official solution to the question has been posted.

Regards,
Ashutosh

gurudabl · Answer

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.

fireagablast · Answer

should just be   *   or  * . 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

ScottTargetTestPrep · Answer

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

Shrey08 · Answer

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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