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Jake, Lena, Fred, John and Inna need to drive home from a corporate re

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marcodonzelli
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Jake, Lena, Fred, John and Inna need to drive home from a corporate re [#permalink] New post   07 Feb 2008, 13:08
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59% (01:57) correct 41% (01:47) wrong based on 373 sessions
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Jake, Lena, Fred, John and Inna need to drive home from a corporate reception in an SUV that can seat 7 people. If only Inna or Jake can drive, how many seat allocations are possible?

A. 30
B. 42
C. 120
D. 360
E. 720
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E
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walker
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Re: Jake, Lena, Fred, John and Inna need to drive home from a corporate re [#permalink] New post   07 Feb 2008, 13:15
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E

[X][YYYYYY]

X: Inna or Jake: \(P^2_1\)
Y: Lena , Fred, John and (Jake or Inna): \(P^6_4\)

\(N=P^2_1*P^6_4=2*\frac{6!}{2!}=6*5*4*3*2=720\)
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Re: Jake, Lena, Fred, John and Inna need to drive home from a corporate re [#permalink] New post   07 Feb 2008, 17:34
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E.720
5 people ,7 seats, only 2 can drive
if inna is in one seat remaining, 4 people can be arranged in 4p4 i.e 4! =24 ways
since any one can drive total ways = 24 *2= 48 ways
4 seats can be chosen out of remaining 6 seats in 6c4 ways = 6!/(4!*2!)= 15 ways
48*15=720
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Re: Jake, Lena, Fred, John and Inna need to drive home from a corporate re [#permalink] New post   07 Feb 2008, 17:16
walker, whats this latex formula business ? lol
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Re: Jake, Lena, Fred, John and Inna need to drive home from a corporate re [#permalink] New post   07 Feb 2008, 19:21
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walker wrote:
E

[X][YYYYYY]

X: Inna or Jake: \(P^2_1\)
Y: Lena , Fred, John and (Jake or Inna): \(P^6_4\)

\(N=P^2_1*P^6_4=2*\frac{6!}{2!}=6*5*4*3*2=720\)


Am I right in saying that the reason we use permutation instead of combination is because the question asks for different seat allocations and A-B-C-D-E is a different "seat allocation" than A-C-B-D-E? (This is the only thing that bugs me for this question... sorry if it sounds stupid.)
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Re: Jake, Lena, Fred, John and Inna need to drive home from a corporate re [#permalink] New post   07 Feb 2008, 19:59
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Basically, are we saying order matters for this problem?
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Re: Jake, Lena, Fred, John and Inna need to drive home from a corporate re [#permalink] New post   07 Feb 2008, 22:49
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marcodonzelli wrote:
Jake , Lena , Fred, John and Inna need to drive home from a corporate reception in an SUV that can seat 7 people . If only Inna or Jake can drive, how many seat allocations are possible?

30

42

120

360

720


please provide a detailed explanation


a case of permutation:
= 2 x 6p4
= 2 (6x5x4x3x2!)/ 2!
= 720
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Re: Jake, Lena, Fred, John and Inna need to drive home from a corporate re [#permalink] New post   08 Feb 2008, 00:40
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pmenon wrote:
walker, whats this latex formula business ? lol


it is a car [X][YYYYYY] :)

X - a seat for a driver.
Y - 6 seats for others.
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Re: Jake, Lena, Fred, John and Inna need to drive home from a corporate re [#permalink] New post   11 Feb 2008, 11:31
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What am I doing wrong.

If Jake is in first spot there are 6! ways to arrange the other 6
If Inna is in first spot there are 6! ways to arrange the other 6

6!+6! = 1440

I know I am not accounting for something and definitely would have picked 720 on the test since 1440 isn't on there, but what am I double counting?

Thanks
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Re: Jake, Lena, Fred, John and Inna need to drive home from a corporate re [#permalink] New post   10 Dec 2014, 16:28
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Hi Bunuel,
I have a doubt here. Appreciate your help.

this question is similar to this problem.

a-family-consisting-of-one-mother-one-father-two-daughters-69657.html


then why permutation used in this problem?



marcodonzelli wrote:
Jake , Lena , Fred, John and Inna need to drive home from a corporate reception in an SUV that can seat 7 people . If only Inna or Jake can drive, how many seat allocations are possible?

30

42

120

360

720


please provide a detailed explanation
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Re: Jake, Lena, Fred, John and Inna need to drive home from a corporate re [#permalink] New post   11 Dec 2014, 06:44
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sunita123 wrote:
Hi Bunuel,
I have a doubt here. Appreciate your help.

this question is similar to this problem.

a-family-consisting-of-one-mother-one-father-two-daughters-69657.html


then why permutation used in this problem?



marcodonzelli wrote:
Jake , Lena , Fred, John and Inna need to drive home from a corporate reception in an SUV that can seat 7 people . If only Inna or Jake can drive, how many seat allocations are possible?

30

42

120

360

720


please provide a detailed explanation


Because the order matters here. But you could solve this with combinations formula too: \(2*C^4_6*4!=720\).

Answer: E.
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Re: Jake, Lena, Fred, John and Inna need to drive home from a corporate re [#permalink] New post   01 May 2019, 18:13
Bunuel wrote:
sunita123 wrote:
Hi Bunuel,
I have a doubt here. Appreciate your help.

this question is similar to this problem.

https://gmatclub.com/forum/a-family-cons ... 69657.html


then why permutation used in this problem?



marcodonzelli wrote:
Jake , Lena , Fred, John and Inna need to drive home from a corporate reception in an SUV that can seat 7 people . If only Inna or Jake can drive, how many seat allocations are possible?

30

42

120

360

720


please provide a detailed explanation


Because the order matters here. But you could solve this with combinations formula too: \(2*C^4_6*4!=720\).

Answer: E.



I still dont understand why order matters here, we have restriction for the drivers seats rest of the seats can be taken by any of the people in any ways . please help me understand. Also when applying combinations approach why are we multiplying by fact.4 in the end
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Re: Jake, Lena, Fred, John and Inna need to drive home from a corporate re [#permalink] New post   29 Sep 2021, 07:46
A common mistake people make in this question is by applying combination instead of permutation. If we arrange using 4! separately after using combinations then also we can get the correct answer.
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Re: Jake, Lena, Fred, John and Inna need to drive home from a corporate re [#permalink] New post   19 Oct 2022, 00:30
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Re: Jake, Lena, Fred, John and Inna need to drive home from a corporate re [#permalink]
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