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

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Jake, Lena, Fred, John and Inna need to drive home from a corporate re  [#permalink]

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New post 07 Feb 2008, 13:08
1
15
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

58% (01:59) correct 42% (01:54) wrong based on 266 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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Re: Jake, Lena, Fred, John and Inna need to drive home from a corporate re  [#permalink]

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New post 07 Feb 2008, 13:15
3
1
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]

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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]

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New post 07 Feb 2008, 17:34
2
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]

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New post 07 Feb 2008, 19:21
3
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]

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New post 07 Feb 2008, 19:59
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]

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New post 07 Feb 2008, 22:49
2
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]

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New post 08 Feb 2008, 00:40
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]

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New post 11 Feb 2008, 11:31
1
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]

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New post 10 Dec 2014, 16:28
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]

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New post 11 Dec 2014, 06:44
2
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]

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