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

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desiguy
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Mike and four friends go to a Knicks game. How many ways can [#permalink] New post   10 Dec 2005, 20:41
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

Please show all workings. :)



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Re: Mike and four friends go to a Knicks game. How many ways can [#permalink] New post   10 Dec 2005, 22:12
4 friends can sit in 4! = 24 ways
mike can pick any of 3 position between two friends

total arrangements: 3 * 24 = 72
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Re: Mike and four friends go to a Knicks game. How many ways can [#permalink] New post   10 Dec 2005, 22:44
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 !! :wink:
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Re: Mike and four friends go to a Knicks game. How many ways can [#permalink] New post   10 Dec 2005, 23:27
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.
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B
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Re: Mike and four friends go to a Knicks game. How many ways can [#permalink] New post   11 Dec 2005, 00:06
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)
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Re: Mike and four friends go to a Knicks game. How many ways can [#permalink] New post   11 Dec 2005, 00:26
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.
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Re: Mike and four friends go to a Knicks game. How many ways can [#permalink] New post   11 Dec 2005, 05:07
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

Please show all workings. :)
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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Re: Mike and four friends go to a Knicks game. How many ways can [#permalink] New post   11 Dec 2005, 09:06
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? :wink:
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desiguy
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Re: Mike and four friends go to a Knicks game. How many ways can [#permalink] New post   11 Dec 2005, 09:40
Good discussion. D is the answer



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Re: Mike and four friends go to a Knicks game. How many ways can [#permalink]
11 Dec 2005, 09:40
Moderator:
yashikaaggarwal
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3137 posts

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