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# Six boys and six girls sit in a row at random.Find the

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Director
Joined: 03 Sep 2006
Posts: 884
Followers: 6

Kudos [?]: 291 [0], given: 33

Six boys and six girls sit in a row at random.Find the [#permalink]  22 Dec 2007, 21:04
Six boys and six girls sit in a row at random.Find the probability that the boys and girls sit alternately.

A) 1/132

B) 1/462

C) 1/623

D) 1/231
CEO
Joined: 17 Nov 2007
Posts: 3574
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 414

Kudos [?]: 2247 [0], given: 359

Expert's post
B

P=2*6P6*6P6/12P12=2*6!*6!/12!=2*6*5*4*3*2/(12*11*10*9*8*7)=1/462
Manager
Joined: 16 Jan 2007
Posts: 73
Followers: 1

Kudos [?]: 10 [0], given: 0

The answer is 'B' i.e. 1/462.

Sample space = 12!

Boys can be seated alternately in 6! ways
Girls can be seated alternately in 6! ways

This can happen in 2 ways as the seats are even .
Likely events = 2* 6!*6!

Probability = Likely events/Sample space
= 2* 6! * 6! /12!
= 1/462
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