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

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

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]
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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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]
1
Kudos
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

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

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

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

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

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