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

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A company will select 2 of the 6 candidates available to work in 2 dif  [#permalink]

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New post Updated on: 13 Aug 2018, 06:28
1
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

47% (02:23) correct 53% (01:58) wrong based on 78 sessions

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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

Learn to use the Keyword Approach in Solving PnC question from the following article:


Article-1: Learn when to “Add” and “Multiply” in Permutation & Combination questions

Article-2: Fool-proof method to Differentiate between Permutation & Combination Questions

Article-3: 3 deadly mistakes you must avoid in Permutation & Combination

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Originally posted by EgmatQuantExpert on 18 Apr 2018, 05:25.
Last edited by EgmatQuantExpert on 13 Aug 2018, 06:28, edited 4 times in total.
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Re: A company will select 2 of the 6 candidates available to work in 2 dif  [#permalink]

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New post Updated on: 23 Apr 2018, 04:39

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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Originally posted by EgmatQuantExpert on 18 Apr 2018, 05:32.
Last edited by EgmatQuantExpert on 23 Apr 2018, 04:39, edited 1 time in total.
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Re: A company will select 2 of the 6 candidates available to work in 2 dif  [#permalink]

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New post 18 Apr 2018, 19:39
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?
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Re: A company will select 2 of the 6 candidates available to work in 2 dif  [#permalink]

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New post 20 Apr 2018, 07:39
[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
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Re: A company will select 2 of the 6 candidates available to work in 2 dif  [#permalink]

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New post 20 Apr 2018, 22:29
aserghe1 wrote:
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?



Hey,


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


Regards,
Saquib
Quant Expert
e-GMAT
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Re: A company will select 2 of the 6 candidates available to work in 2 dif  [#permalink]

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New post 23 Apr 2018, 04:59
Hey Everyone,

Official solution to the question has been posted.

Regards,
Ashutosh
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Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

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