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 Post subject: Book no 12, Combinatorics and Probability, question 79Posted: Sun Aug 15, 2010 12:24 am

Joined: Wed Oct 28, 2009 1:08 am
Posts: 1
Book no 12, Combinatorics and Probability, question 79, page 128

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?

My question is:
the solution states that "since the driver's seat is occupied, we have to allocate the remaining 4 people among the 6 passenger seats. Because the order of the seat assignments is important, we will use the permutations formula"

Considering the fact that the restriction placed on the question is that the driver's seat can only be occupied by either Inna or Jake, If we were to place Jake in the driver's seat, why would the order of selection matter when we are choosing where to place the remaining 4 passengers among 6 seats?

In other words, why do we need to use the permutations formula instead of the combinations formula?

The way I solved this problem is illustrated below -
Assuming Jake is the driver,
We have 4 remaining people that can be seated among 6 seats
Order of selection for the REMAINING people does not matter
Hence, combinations formula is used to find out number of ways 4 people can be seated in 6 places
That is, 6C4 = 6!/(4!x2!) = 15

Now since Inna could also be the driver, we have another set of seating arrangments:
therefore total number of seat allocations = 15x2 = 30

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 Post subject: Re: Book no 12, Combinatorics and Probability, question 79Posted: Sun Aug 15, 2010 8:52 am

Joined: Thu Feb 12, 2009 6:32 pm
Posts: 497
The term "allocation" implies that we are concerned with arrangement of the occupants, and so we use the permutation formula instead of the combination one.

Veritas Help

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 Post subject: Re: Book no 12, Combinatorics and Probability, question 79Posted: Sat May 12, 2012 10:56 pm

Joined: Sat May 12, 2012 10:54 pm
Posts: 1
I don't understand why the 2 is used for K. I know that:
6 = number of seats to be filled
4 = the number of people from which to fill the seats
2 = ????

Can anyone help?

Thanks

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 Post subject: Re: Book no 12, Combinatorics and Probability, question 79Posted: Tue May 15, 2012 6:33 pm

Joined: Thu Feb 12, 2009 6:32 pm
Posts: 497
If Inna drives we have 6 seats remaining with which to seat 4 people.

The are 6*5*4*3 ways to do this (6 choice for the first person) * (5 choice for the second) * (4 for the third) * (3 for the 4th) = 360

If Jake drives, there are also 360 arrangements (same analysis as the above)

So 360 + 360 = 720

- Veritas Help

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