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

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

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