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# How many different carpool possibilities exist for 12 coworkers from

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Math Expert
Joined: 02 Sep 2009
Posts: 56261
How many different carpool possibilities exist for 12 coworkers from  [#permalink]

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13 Dec 2016, 07:04
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Difficulty:

5% (low)

Question Stats:

88% (00:57) correct 12% (01:11) wrong based on 322 sessions

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How many different carpool possibilities exist for 12 coworkers from the same neighborhood?

(1) Each of the three cars that will be used for carpooling seats exactly 4 people.
(2) If 2 of the coworkers took the day off, there would be fewer carpool possibilities.

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Re: How many different carpool possibilities exist for 12 coworkers from  [#permalink]

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13 Dec 2016, 22:00
1
Bunuel wrote:
How many different carpool possibilities exist for 12 coworkers from the same neighborhood?

(1) Each of the three cars that will be used for carpooling seats exactly 4 people.
(2) If 2 of the coworkers took the day off, there would be fewer carpool possibilities.

CARPOOL MEANING: an arrangement between people to make a regular journey in a single vehicle, typically with each person taking turns to drive the others.

Once you understand the meaning it is easy to identify the question.

Stat 1: There are three cars with 4 seats...then out of 12 workers...Since there is no restriction on the workers...

in the first car = 12C4 possibilities..
second car = 12C4
third car = 12C4.... Sufficient.

Stat 2: We don't have enough information about the cars here but we have 10 worker information...Hence insufficient.

IMO option A.
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Re: How many different carpool possibilities exist for 12 coworkers from  [#permalink]

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18 Apr 2017, 22:24
I think it should be :

In first car, 12C4
Second car, 8C4
The remaining four people would automatically get the third car.

For each combination of first car, there are 8C4 combinations of second car (and automatic selection for third).
Therefore, total number of car pooling possibilities will be 12C4 * 8C4.
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Joined: 31 Dec 2017
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Location: India
Concentration: Entrepreneurship, Technology
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Re: How many different carpool possibilities exist for 12 coworkers from  [#permalink]

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17 Mar 2018, 01:06
pristine29 wrote:
I think it should be :

In first car, 12C4
Second car, 8C4
The remaining four people would automatically get the third car.

For each combination of first car, there are 8C4 combinations of second car (and automatic selection for third).
Therefore, total number of car pooling possibilities will be 12C4 * 8C4.

I too think this is the correct calculation. Can we please get an expert opinion on this pls??
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Re: How many different carpool possibilities exist for 12 coworkers from  [#permalink]

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17 Mar 2018, 01:15
arunalo wrote:
pristine29 wrote:
I think it should be :

In first car, 12C4
Second car, 8C4
The remaining four people would automatically get the third car.

For each combination of first car, there are 8C4 combinations of second car (and automatic selection for third).
Therefore, total number of car pooling possibilities will be 12C4 * 8C4.

I too think this is the correct calculation. Can we please get an expert opinion on this pls??

I'm not an expert but am certain that the highlighted calculations are correct.

The total number of car-pooling possibilities must be 12c4*8c4*1(for 4c4)
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Re: How many different carpool possibilities exist for 12 coworkers from  [#permalink]

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27 Mar 2018, 18:16
Bunuel niks18 chetan2u

Quote:
How many different carpool possibilities exist for 12 coworkers from the same neighborhood?

(1) Each of the three cars that will be used for carpooling seats exactly 4 people.
(2) If 2 of the coworkers took the day off, there would be fewer carpool possibilities.

Were this a PS problem would question stem and statement A resulted in 3 * $$12C4$$ ?
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Posts: 7764
Re: How many different carpool possibilities exist for 12 coworkers from  [#permalink]

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27 Mar 2018, 20:23
Bunuel niks18 chetan2u

Quote:
How many different carpool possibilities exist for 12 coworkers from the same neighborhood?

(1) Each of the three cars that will be used for carpooling seats exactly 4 people.
(2) If 2 of the coworkers took the day off, there would be fewer carpool possibilities.

Were this a PS problem would question stem and statement A resulted in 3 * $$12C4$$ ?

This basically asks to distribute 12 in 3 groups of 4 each..
First group-12C4
Second - 8C4.. 4 out of remaining 8
Third remaining 4
So 12C4*8C4..

Direct formula for these (ax) items to be distributed in a groups of x items each is (ax)!/(x!)^a... Here (3*4)!/(4!)^3

12C4*8C4=12!/(8!4!) * 8!/(4!4!)=12!/(4!)^3..

You will find this in my signature about combinations
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Re: How many different carpool possibilities exist for 12 coworkers from   [#permalink] 27 Mar 2018, 20:23
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