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

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CEO
Joined: 15 Aug 2003
Posts: 3467
Followers: 61

Kudos [?]: 718 [0], given: 781

There are 2 brothers among a group of 20 persons. In how [#permalink]  07 Oct 2003, 19:11
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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!
SVP
Joined: 03 Feb 2003
Posts: 1607
Followers: 6

Kudos [?]: 84 [0], given: 0

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!
SVP
Joined: 30 Oct 2003
Posts: 1794
Location: NewJersey USA
Followers: 5

Kudos [?]: 43 [0], given: 0

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!
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