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There are 2 brothers among a group of 20 persons. In how

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There are 2 brothers among a group of 20 persons. In how [#permalink] New post 07 Oct 2003, 20:11
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There are 2 brothers among a group of 20 persons. In how many ways can the group be arranged around a circle so that there is exactly one person between the two brothers?

1) 2 * 19!
2) 18! * 18
3) 19! * 18
4) 2 * 18!
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 [#permalink] New post 07 Oct 2003, 23:28
fix one person and the brothers B1 P B2 = 2 ways to do so.
other 17 people= 17!
Each person out of 18 can be fixed between the two=18

thus, 2*17!*18=2*18!
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 [#permalink] New post 08 Jan 2004, 10:40
Fix the postion of two brothers. This leaves us with 18 people.
So there 18 ways in which a person can sit between two brother. Now swap thsoe bothers we get another 18 ways
So combinations = 2 * 18.
Consider the groupe of three people a single entity
we have another 17 people left so there are 18 entities to be arranged
Around a circle. Tis can be done in (18-1)! = 17!

Total no of ways = 2 * 18 * 17! = 2 * 18!
  [#permalink] 08 Jan 2004, 10:40
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