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

Question

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

walker · Accepted Answer

E

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

nikunjhd · Answer

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

pmenon · Answer

walker, whats this latex formula business ? lol

aimecon · Answer

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.)

jimmyjamesdonkey · Answer

Basically, are we saying order matters for this problem?

GMAT TIGER · Answer

a case of permutation:
= 2 x 6p4
= 2 (6x5x4x3x2!)/ 2!
= 720

walker · Answer

it is a car

X - a seat for a driver. Y - 6 seats for others.

terp26 · Answer

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

sunita123 · Answer

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?

Bunuel · Answer

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

Answer: E.

Mohammad Ali Khan · Answer

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

kanishaksharma · Answer

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.

bumpbot · Answer

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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

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