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

Question

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.

duttsit · Answer

4 friends can sit in 4! = 24 ways
mike can pick any of 3 position between two friends

total arrangements: 3 * 24 = 72

ywilfred · Answer

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:

HIMALAYA · Answer

what this "between two friends" means? i thought mike's position as under.

A.B.mike.C.D.

Mike always maintaines this position.

GMATT73 · Answer

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)

duttsit · Answer

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.

Yurik79 · Answer

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

HIMALAYA · Answer

dutt, your music is beautiful but i could not differentiate it whether it from gitar or ektara? :wink:

desiguy · Answer

Good discussion. D is the answer

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

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