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In a certain company the board of directors has been given the respons

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New post 12 Aug 2017, 00:57
3
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A
B
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E

Difficulty:

  25% (medium)

Question Stats:

70% (01:19) correct 30% (01:21) wrong based on 173 sessions

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In a certain company the board of directors has been given the responsibility of nominating 3 key positions (one director and two identical positions in the senior management). The board will select 1 of 10 candidates eligible to fill the position of director and 2 of 8 candidates eligible to fill the 2 identical positions in the senior management. How many different sets of 3 candidates are there to fill 3 key positions assuming that no candidate is eligible for more than one post?

A. 70
B. 140
C. 280
D. 560
E. 1120
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New post 12 Aug 2017, 02:15
10C1 X 8C2.
That's 280.

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New post 14 Mar 2018, 09:56
Since we can select 1 of 10 candidates to fill the position of director
Number of ways to achieve that = 10C1=10 ways
Similarly we have to select 2 of 8 candidates to fill the position in senior management which can be achieved in 8C2=28 ways
Number of ways to select 1 director “AND” number of ways of selecting 2 senior managers = 10 × 28 = 280 ways

Ans.:- C
:)
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New post 16 Mar 2018, 05:06
Hi. I am not at all good with Combi and Perm. so please bear with me.

I opted 560 as my answer. My question is, when there are 3 positions and for 1st position we can fill it in 10 ways, why cant we take the 2nd and 3rd position to be filled in 8 and 7 ways respectively. that is:-

10 8 7 = 560.

I hope i was able to make myself clear.
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New post 19 Mar 2018, 16:08
DHAR wrote:
In a certain company the board of directors has been given the responsibility of nominating 3 key positions (one director and two identical positions in the senior management). The board will select 1 of 10 candidates eligible to fill the position of director and 2 of 8 candidates eligible to fill the 2 identical positions in the senior management. How many different sets of 3 candidates are there to fill 3 key positions assuming that no candidate is eligible for more than one post?

A. 70
B. 140
C. 280
D. 560
E. 1120


The number of ways to select the director is 10P1 = 10.

The number of ways to select the senior management is is 8C2 = (8 x 7)/2! = 28.

So, the total number of ways to fill the positions is 10 x 28 = 280.

Answer: C
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Re: In a certain company the board of directors has been given the respons  [#permalink]

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New post 22 Mar 2018, 18:40
sandysilva wrote:
Hi. I am not at all good with Combi and Perm. so please bear with me.

I opted 560 as my answer. My question is, when there are 3 positions and for 1st position we can fill it in 10 ways, why cant we take the 2nd and 3rd position to be filled in 8 and 7 ways respectively. that is:-

10 8 7 = 560.

I hope i was able to make myself clear.



I also solved in above manner. Why 560 is not correct ?
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Re: In a certain company the board of directors has been given the respons  [#permalink]

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New post 15 Jan 2019, 09:36
@chetan2u:-what if identical positions was not mentioned in the question? Would we have then taken 10p1 X 8p2?
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Re: In a certain company the board of directors has been given the respons   [#permalink] 15 Jan 2019, 09:36
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