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In how many ways can you seat 3 people in a row of 101

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Current Student
Joined: 31 Aug 2007
Posts: 368

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In how many ways can you seat 3 people in a row of 101 [#permalink]

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02 Oct 2007, 12:46
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

In how many ways can you seat 3 people in a row of 101 chairs, if they are all to sit together?

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VP
Joined: 08 Jun 2005
Posts: 1144

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02 Oct 2007, 12:52
(101-2)! = 99!

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Current Student
Joined: 31 Aug 2007
Posts: 368

Kudos [?]: 163 [0], given: 1

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02 Oct 2007, 12:58
shouldn't it be 6*99?

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VP
Joined: 08 Jun 2005
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02 Oct 2007, 13:04
young_gun wrote:
shouldn't it be 6*99?

Yes ! you are correct it should be (101-2)!*3! of course !

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Current Student
Joined: 31 Aug 2007
Posts: 368

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02 Oct 2007, 13:05
but I do not see why you are making it 99!, i think it should just be 3!*99.

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Director
Joined: 09 Aug 2006
Posts: 754

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02 Oct 2007, 13:06
KillerSquirrel wrote:
young_gun wrote:
shouldn't it be 6*99?

Yes ! you are correct it should be (101-2)!*3! of course !

I'm very weak w/ comb. q's. Can you please explain what's going on here? How did u figure out the solution? Thanks.

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Current Student
Joined: 31 Aug 2007
Posts: 368

Kudos [?]: 163 [0], given: 1

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02 Oct 2007, 13:32
Can you pls explain how the answer should be:
(101-2)!*3! of course !

I believe it should just be 99*3!.

If we had 5 seats and 2 people to place sitting next to each other, without much calculation it would be:

(_ _) _ _ _ 1
_ (_ _) _ _ 1
_ _ (_ _) _ 1
_ _ _ (_ _) 1

4*2!=8 different ways (not 4!*2!). Is this not correct?

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VP
Joined: 08 Jun 2005
Posts: 1144

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02 Oct 2007, 14:00
yes ! you are correct.

If we see the three people as one the question really asks for "In how many ways can you sit one person in a row of 99 empty chairs" clearly the answer is 99. Now since we can arrange the three people in 3! = 6 ways within themselves then:

99*3! = 99*6 = is the answer.

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Director
Joined: 17 Sep 2005
Posts: 901

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03 Oct 2007, 08:21
We don't have to arrange the chairs, we have to make three people sit together in different possible ways.

3 people can sit together in 3! ways.
Now we have (101 - 2) = 99 different seats to be occupied by them.

So total no of ways = 99*3!

- Brajesh

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03 Oct 2007, 08:21
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