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Joey is planning to throw a small party

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Joey is planning to throw a small party [#permalink]

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New post 22 Apr 2015, 08:37
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Difficulty:

  45% (medium)

Question Stats:

59% (00:51) correct 41% (01:05) wrong based on 86 sessions

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Joey is planning to throw a small party and for that he needs to do the following tasks:
I. Decide guest list
II. Send invites
III. Arrange catering
IV. Decide the venue
V. Rent a music system
The tasks can be done in any order as long as the invites are sent after the guest list is decided. In how many ways can Joey do the five tasks listed above?

    A. 24
    B. 48
    C. 60
    D. 120
    E. 240
[Reveal] Spoiler: OA
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Re: Joey is planning to throw a small party [#permalink]

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New post 22 Apr 2015, 09:13
Expert's post
PrepTap wrote:
Joey is planning to throw a small party and for that he needs to do the following tasks:
I. Decide guest list
II. Send invites
III. Arrange catering
IV. Decide the venue
V. Rent a music system
The tasks can be done in any order as long as the invites are sent after the guest list is decided. In how many ways can Joey do the five tasks listed above?

    A. 24
    B. 48
    C. 60
    D. 120
    E. 240


These 5 tasks can be arranged in 5! = 120 ways. In half of them invites are sent after the guest list is decided and in half of them before. So, there are total of 120/2 = 60 ways to arrange the task so that the invites are sent after the guest list is decided.

Answer: C.

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Re: Joey is planning to throw a small party [#permalink]

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New post 28 Nov 2017, 13:57
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Hi All,

We're told that there are 5 tasks to be completed. IF there were no 'restrictions', then there would be 5! = (5)(4)(3)(2)(1) = 120 different possible 'orders' for those 5 tasks. However, there IS a 'restriction' - the invites can only be sent AFTER the guest list is determined. In the original 120 possible orders, the 5 tasks are done one-at-a-time, so HALF of the options had the invites sent BEFORE the guest list and HALF of the options had the invites sent AFTER the guest list. Thus, there are (1/2)(120) = 60 possible orders in which the invites are sent after the guest list.

Final Answer:
[Reveal] Spoiler:
C


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Re: Joey is planning to throw a small party   [#permalink] 28 Nov 2017, 13:57
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