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A 3-people committee, including a director, a vice director, and a

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A 3-people committee, including a director, a vice director, and a  [#permalink]

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New post 09 Aug 2019, 08:01
3
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00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

51% (00:53) correct 49% (00:57) wrong based on 39 sessions

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A 3-people committee, including a director, a vice director, and a secretary, is to be selected from 12 members. How many different committees are possible?

(A) 220

(B) 330

(C) 440

(D) 660

(E) 1320

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A 3-people committee, including a director, a vice director, and a  [#permalink]

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New post 09 Aug 2019, 08:24
12C3*3!=220*6=1320

IMO E

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Re: A 3-people committee, including a director, a vice director, and a  [#permalink]

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New post 09 Aug 2019, 09:23
Kinshook wrote:
12C3*3!=220*6=1320

IMO E

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Why do we have to multiply 220 with 3!?
With 12C3 we calculate how many objects (=3) we want to select from a larger set of 12 objects correct?
This needs to be multiplied by 3! because every person can be arranged if he/she has been selected to be part of the group another 3! times?
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Re: A 3-people committee, including a director, a vice director, and a  [#permalink]

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New post 09 Aug 2019, 10:58
Luca1111111111111 wrote:
Kinshook wrote:
12C3*3!=220*6=1320

IMO E

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Why do we have to multiply 220 with 3!?
With 12C3 we calculate how many objects (=3) we want to select from a larger set of 12 objects correct?
This needs to be multiplied by 3! because every person can be arranged if he/she has been selected to be part of the group another 3! times?


3 persons out of 12 can be selected in 12C3 = 220 ways.
But these 3 selected persons can be further assigned ranks in the committee in 3! Ways.
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Re: A 3-people committee, including a director, a vice director, and a  [#permalink]

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New post 09 Aug 2019, 11:31
3 out of 12 can be selected in 12C3 ways.
Then these three can further be arranged in 3! ways.
So total 220x6=1320
E is the answer.

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Re: A 3-people committee, including a director, a vice director, and a  [#permalink]

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New post 09 Aug 2019, 11:39
12P3 because each committee requires a distinct arrangement

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Re: A 3-people committee, including a director, a vice director, and a   [#permalink] 09 Aug 2019, 11:39
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