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An admission office director has 7 times available for interviews at a

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Bunuel
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An admission office director has 7 times available for interviews at a [#permalink] New post   17 Jun 2019, 00:46
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An admission office director has 7 times available for interviews at afternoon. There are 12 students disputing the vacancies. In how many different ways can the director set up his/her program (answering the candidates individually)?

(A) 12!/(5!7!)
(B) 12!/7!
(C) 12!/5!
(D) 12!
(E) 12^7
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C
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Re: An admission office director has 7 times available for interviews at a [#permalink] New post   17 Jun 2019, 09:10
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IMO A ; 12c7 ways possible to arrange interviews
12!/(5!7!)

Bunuel wrote:
An admission office director has 7 times available for interviews at afternoon. There are 12 students disputing the vacancies. In how many different ways can the director set up his/her program (answering the candidates individually)?

(A) 12!/(5!7!)
(B) 12!/7!
(C) 12!/5!
(D) 12!
(E) 12^7
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IanStewart
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Re: An admission office director has 7 times available for interviews at a [#permalink] New post   17 Jun 2019, 10:39
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I don't think the wording is sufficiently clear, but I'd assume the director has 12 choices for the first open time in her schedule, 11 choices for the next, and so on. Since she can only interview seven people in total, the number of possible schedules will be (12)(11)(10)(9)(8)(7)(6), which is equal to 12!/5!.
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Re: An admission office director has 7 times available for interviews at a [#permalink] New post   17 Jun 2019, 20:00
I am confused again!

Why is it not 12!/(5!7!)?
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Re: An admission office director has 7 times available for interviews at a [#permalink] New post   18 Jun 2019, 08:02
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The answer is C. 12!/5!. Why? The director has 12 options for time slot 1, 11 for time slot 2,10 for time slot 3,and so on making it 12*11*10*8*7*6*5 which is equivalent to 12P5 or 12!/(12-7)! Hence answer is C
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Re: An admission office director has 7 times available for interviews at a [#permalink] New post   19 Jun 2019, 06:06
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Since, this will involve arrangements as well. Thus, possible ways are 12P7 => 12!/5! (C)
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Re: An admission office director has 7 times available for interviews at a [#permalink] New post   19 Jun 2019, 13:57
What is the correct answer for this. Is it 12!/5! or 12!/(5!7!) . Since arrangement is not necessary here, we can easily mark 12c7 in this case
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Re: An admission office director has 7 times available for interviews at a [#permalink] New post   19 Jun 2019, 18:53
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Bunuel wrote:
An admission office director has 7 times available for interviews at afternoon. There are 12 students disputing the vacancies. In how many different ways can the director set up his/her program (answering the candidates individually)?

(A) 12!/(5!7!)
(B) 12!/7!
(C) 12!/5!
(D) 12!
(E) 12^7



The number of ways to set up the program is 12P7 = 12!/(12 - 7)! = 12!/5!.

Answer: C
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Re: An admission office director has 7 times available for interviews at a [#permalink]
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