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Will decides to attend a basketball game with four friends.

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Will decides to attend a basketball game with four friends.  [#permalink]

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New post 17 Jan 2014, 07:21
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Will decides to attend a basketball game with four friends.
If the party of five sits together in five consecutive seats, and Will must NOT sit in between two of his friends, how many ways
can the five friends be arranged?

A) 24
B) 36
C) 48
D) 72
E) 120
Intern
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Re: Will decides to attend a basketball game with four friends.  [#permalink]

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New post 17 Jan 2014, 07:22
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Found this a nice (medium difficulty) combinatorics question with constraints and thought worthwhile sharing.
The way I solved this is as follows:

1. There are five people sitting in five seats next to each other. Let each seat be "X": XXXXX

2. Now Will cannot sit in between of his friends. Let "W" be Will and each his four friends be "F".
This means Will can only sit at the edge. There are two ways: WFFFF or FFFFW.

3. In the first instance, Will sits on the left and there are 4! ways for his friends to sit
or (remember "or" means adding) Will sits on the right and there are 4! ways for his friends to sit.

4! = 4x3x2 = 24. Since we have this two times ("or") we need to add for both instances: 24 + 24 = 48.
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Re: Will decides to attend a basketball game with four friends.  [#permalink]

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New post 17 Jan 2014, 21:47
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BabySmurf wrote:
Will decides to attend a basketball game with four friends.
If the party of five sits together in five consecutive seats, and Will must NOT sit in between two of his friends, how many ways
can the five friends be arranged?

A) 24
B) 36
C) 48
D) 72
E) 120


Will have to sit at either of the ends.

If will sits on the left most corner, then other 4 friends can be arranged in 4! = 24
Will can also sit on the other end, then another 4! ways we can arrange.
So total number of ways = 24+24 = 48 - Option C)
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Re: Will decides to attend a basketball game with four friends.  [#permalink]

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New post 02 Sep 2018, 06:15
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Re: Will decides to attend a basketball game with four friends.   [#permalink] 02 Sep 2018, 06:15
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