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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: 3470
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Kudos [?]: 697 [0], given: 781

A team of 8 students goes on an excursion, in two cars, of [#permalink]  07 Oct 2003, 19:44
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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

SVP
Joined: 03 Feb 2003
Posts: 1611
Followers: 6

Kudos [?]: 74 [0], given: 0

8=4+4 => 8C4=70, I would divide 70 by 2 because doubling effecr is here
8=5+3 => 8C5=56

70+56=126
CEO
Joined: 15 Aug 2003
Posts: 3470
Followers: 61

Kudos [?]: 697 [0], given: 781

Re: PS : Counting Methods ( Two Cars , 8 Students) [#permalink]  08 Oct 2003, 16:30
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
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Joined: 20 Sep 2003
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Location: NY, NY
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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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CEO
Joined: 15 Aug 2003
Posts: 3470
Followers: 61

Kudos [?]: 697 [0], given: 781

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?
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