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# Mike and four friends go to a Knicks game. How many ways can

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Senior Manager
Joined: 11 May 2004
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Mike and four friends go to a Knicks game. How many ways can [#permalink]  10 Dec 2005, 19:41
Mike and four friends go to a Knicks game. How many ways can they sit together so that Mike always sits between two friends?

6
24
48
72
120

VP
Joined: 22 Aug 2005
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Location: CA
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4 friends can sit in 4! = 24 ways
mike can pick any of 3 position between two friends

total arrangements: 3 * 24 = 72
_________________

Whether you think you can or think you can't. You're right! - Henry Ford (1863 - 1947)

GMAT Club Legend
Joined: 07 Jul 2004
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Location: Singapore
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Assuming the seat are: 1,2,3,4,5

Mike cannot take seat 1 and 5, since he will not be between 2 friends.

He can occupy 2,3 or 4. For each seat, say seat 2, there are 4! ways to arrange his friends.

Soln: 3 * 4!= 72 arrangements. (Note: 4! is permutation)

And i hope larry brown starts finding a winning starting 5 !!
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Joined: 05 Apr 2005
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duttsit wrote:
4 friends can sit in 4! = 24 ways
mike can pick any of 3 position between two friends
total arrangements: 3 * 24 = 72

what this "between two friends" means? i thought mike's position as under.

A.B.mike.C.D.

Mike always maintaines this position.
Current Student
Joined: 29 Jan 2005
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Mike can`t sit on any of the outer seats.

_ _ _ _ _

Mike is X so;

_X_ _ _

or

_ _ X _ _

or

_ _ _ X_

Four friends can sit 4! ways= 24
Mike can choose any one of 3 ways, so 3*24=72

(D)
VP
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HIMALAYA wrote:
duttsit wrote:
4 friends can sit in 4! = 24 ways
mike can pick any of 3 position between two friends
total arrangements: 3 * 24 = 72

what this "between two friends" means? i thought mike's position as under.

A.B.mike.C.D.

Mike always maintaines this position.

between two friends, here indicates that he is always embedded by two frields(cannot be sitting at the corners)

as matt shown, there can be 3 such positions.
_________________

Whether you think you can or think you can't. You're right! - Henry Ford (1863 - 1947)

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Re: Arrangements [#permalink]  11 Dec 2005, 04:07
desiguy wrote:
Mike and four friends go to a Knicks game. How many ways can they sit together so that Mike always sits between two friends?

6
24
48
72
120

All possible ways 5!=120
The cases when Mike is not between two of his friends
Mike __ __ __ __ 4!=24
__ __ __ __ Mike 4!=24
Hence The cases when Mike is sitting between two friends is 120-24-24=72
My vote for D
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Joined: 05 Apr 2005
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duttsit wrote:
HIMALAYA wrote:
duttsit wrote:
4 friends can sit in 4! = 24 ways
mike can pick any of 3 position between two friends
total arrangements: 3 * 24 = 72

what this "between two friends" means? i thought mike's position as under.

A.B.mike.C.D.

Mike always maintaines this position.

between two friends, here indicates that he is always embedded by two frields(cannot be sitting at the corners)

as matt shown, there can be 3 such positions.

dutt,
your music is beautiful but i could not differentiate it whether it from gitar or ektara?
Senior Manager
Joined: 11 May 2004
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Location: New York
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Kudos [?]: 14 [0], given: 0

Good discussion. D is the answer
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