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# A team of 8 students goes on an excursion, in two cars, of

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CEO
Joined: 15 Aug 2003
Posts: 3454

Kudos [?]: 904 [0], given: 781

A team of 8 students goes on an excursion, in two cars, of [#permalink]

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07 Oct 2003, 20:44
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A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?

1) 9
2) 26
3) 126
4) 3920

Kudos [?]: 904 [0], given: 781

SVP
Joined: 03 Feb 2003
Posts: 1603

Kudos [?]: 299 [0], given: 0

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07 Oct 2003, 23:38
8=4+4 => 8C4=70, I would divide 70 by 2 because doubling effecr is here
8=5+3 => 8C5=56

70+56=126

Kudos [?]: 299 [0], given: 0

CEO
Joined: 15 Aug 2003
Posts: 3454

Kudos [?]: 904 [0], given: 781

Re: PS : Counting Methods ( Two Cars , 8 Students) [#permalink]

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08 Oct 2003, 17:30
praetorian123 wrote:
A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?

1) 9
2) 26
3) 126
4) 3920

we have two cases

1. divide 8 into 5 and 3

# of ways = 8! /(5!*3!) = 56

2. divide 8 into 4 and 4

# of ways = 8! / (4! *4!) = 70

total = > 126

stolyar, i dont think we need to divide the 70 by 2...
for example, if you have ABCD and EFGH ...both of these groups when selected will have unique combinations...

thanks
praetorian

Kudos [?]: 904 [0], given: 781

Intern
Joined: 20 Sep 2003
Posts: 22

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Location: NY, NY

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15 Oct 2003, 18:25
if we have one car with 5 spaces and the other with 3 spaces for 8 people, I would you say that there are 70 diferent ways to travel, not 140, right? Because the 3 left from the 5-space car were already counted in the 3-space car.
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Yoda
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Try not. Do or Not Do, there is no try!

Kudos [?]: [0], given: 0

CEO
Joined: 15 Aug 2003
Posts: 3454

Kudos [?]: 904 [0], given: 781

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16 Oct 2003, 02:15
Yoda wrote:
if we have one car with 5 spaces and the other with 3 spaces for 8 people, I would you say that there are 70 diferent ways to travel, not 140, right? Because the 3 left from the 5-space car were already counted in the 3-space car.

dont understand what you are trying to say.

do you agree with my answer?

Kudos [?]: 904 [0], given: 781

16 Oct 2003, 02:15
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# A team of 8 students goes on an excursion, in two cars, of

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