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Six people are on an elevator that stops at exactly 6 floors

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Six people are on an elevator that stops at exactly 6 floors [#permalink] New post 19 Feb 2012, 05:02
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Six people are on an elevator that stops at exactly 6 floors. What is the probability that exactly one person will push the button for each floor?

(A) 6!/6^6
(B) 6^6/6!
(C) 6/6!
(D) 6/6^6
(E) 1/6^6
[Reveal] Spoiler: OA
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Re: Six people [#permalink] New post 19 Feb 2012, 05:11
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caliber23 wrote:
Six people are on an elevator that stops at exactly 6 floors. What is the probability that exactly one person will push the button for each floor?

(A) 6!/6^6
(B) 6^6/6!
(C) 6/6!
(D) 6/6^6
(E) 1/6^6


Each person out of 6 has 6 options, hence total # of outcomes is 6^6;

Favorable outcomes will be 6!, which is # of ways to assign 6 different buttons to 6 people:
1-2-3-4-5-6 (floors)
A-B-C-D-E-F (persons)
B-A-C-D-E-F (persons)
B-C-A-D-E-F (persons)
...
So basically # of arrangements of 6 distinct objects: 6!.

P=favorable/total=6!/6^6

Answer: A.
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Re: Six Six people are on an elevator that stops at exactly 6 [#permalink] New post 19 Feb 2012, 05:55
Hi, could you please tell me the mistake in the following logic?

First person entering pushes one button, it doesn't matter which: p=1
Second person pushes a button that has not been pressed before. Since one is already pushed, only 5 remain: p=5/6
Same logic for third person: p=4/6
.
.
.

This leaves us with The probability of all pushing a different button of: 1*5/6*4/6*4/6*2/6*1/6 or 5!/6^5

Where's the mistake?
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Re: Six Six people are on an elevator that stops at exactly 6 [#permalink] New post 19 Feb 2012, 05:57
Totol possibilities: 6^6 (Each person may push each level the button)

First floor: 6 person
second floor: 5 person
...
= 6!

Possibility: 6!/6^6 --> A
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Re: Six Six people are on an elevator that stops at exactly 6 [#permalink] New post 19 Feb 2012, 10:48
Expert's post
Gwydion wrote:
Hi, could you please tell me the mistake in the following logic?

First person entering pushes one button, it doesn't matter which: p=1
Second person pushes a button that has not been pressed before. Since one is already pushed, only 5 remain: p=5/6
Same logic for third person: p=4/6
.
.
.

This leaves us with The probability of all pushing a different button of: 1*5/6*4/6*4/6*2/6*1/6 or 5!/6^5

Where's the mistake?


There is no mistake: 6!/6^6=(5!*6)/(6^5*6)=5!/6^5, the same answers.
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Re: Six people are on an elevator that stops at exactly 6 floors [#permalink] New post 07 Jun 2013, 06:03
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Re: Six Six people are on an elevator that stops at exactly 6 [#permalink] New post 07 Jun 2013, 06:52
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Gwydion wrote:
Hi, could you please tell me the mistake in the following logic?

First person entering pushes one button, it doesn't matter which: p=1
Second person pushes a button that has not been pressed before. Since one is already pushed, only 5 remain: p=5/6
Same logic for third person: p=4/6
.
.
.

This leaves us with The probability of all pushing a different button of: 1*5/6*4/6*4/6*2/6*1/6 or 5!/6^5

Where's the mistake?


Expanding on Gwydion's post - it is true that p=1, but because the answers all have 6 in them, the first person should be written as p=6/6 to make it easier to see the answer:

First person walks in and can push any button (6/6)
Probability that second person will press any of the remaining 5 buttons (5/6)
Probability that third person will press any of the remaining 4 buttons (4/6)
Probability that fourth person will press any of the remaining 3 buttons (3/6)
Probability that fifth person will press either of the remaining 2 buttons (2/6)
Probability that sixth person will press the remaining button (1/6)

\frac{6}{6} * \frac{5}{6} * \frac{4}{6} * \frac{3}{6} * \frac{2}{6} * \frac{1}{6} = \frac{6*5*4*3*2*1}{6*6*6*6*6*6} = \frac{6!}{6^6}

Answer is A
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Re: Six people are on an elevator that stops at exactly 6 floors [#permalink] New post 10 Jul 2014, 01:31
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Six people are on an elevator that stops at exactly 6 floors   [#permalink] 10 Jul 2014, 01:31
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