Probability Question

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abhijeetsinghai: Senior | Next Rank: 100 Posts; Posts: 39; Joined: Fri Jul 04, 2008 8:54 am; Location: US; Thanked: 1 times; GMAT Score:700

by abhijeetsinghai » Mon Jan 26, 2009 6:04 am

Six boys and six girls sit slong s line alternatively in x ways and along a circle in y ways(again alternatively) , then find the relation between x and y .

a. x = 12y
b. x = 2y
c. x = 6y
d. x= 8y

OA:[spoiler]a

please tell me the approach.thanx !![/spoiler]

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Source: Beat The GMAT — Problem Solving | Mon Jan 26, 2009 6:04 am

Uri: Master | Next Rank: 500 Posts; Posts: 229; Joined: Tue Jan 13, 2009 6:56 am; Thanked: 8 times; GMAT Score:700

by Uri » Tue Feb 10, 2009 8:24 am

Scenario I: Straight line arrangement
6 boys can sit in 6 seats in 6! ways
6 girls can sit in 6 seats in 6! ways
Either of the groups can take the first seat.
So, the total no. of possible arrangements is 2*6!*6!
This is x.

Scenario II: Circular arrangement
Let us first offer the sit to a girl! Once this girl sits, the rest of the girls can sit in 5! ways, keeping one seat vacant between each one of them.
Once the girls are seated, the boys can be arranged in 6 seats in 6! ways.
Since this is a circular arrangement, we don't have to consider whether the boy sits first or the girl.
So, the number of arrangements= 5! * 6!
This is y.

Therefore x/y= 12
or x=12y

Can anyone verify whether the above explanation is correct? I am very weak in Permutation & Combination. But still, somehow gathered enough courage to try this problem

Please help :!:

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ontopofit: Senior | Next Rank: 100 Posts; Posts: 68; Joined: Sun Dec 21, 2008 12:00 am; Thanked: 3 times

by ontopofit » Tue Feb 10, 2009 12:49 pm

yes it's correct...besides there is direct formula that number of permutations in circular arr. is (n-1)!.....i.e in this case y=11! and x=12!.hence x=12y.

however, i appreciate the way u have dun it. its better not to depend too much on direct formulas.

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raunekk: Legendary Member; Posts: 1159; Joined: Wed Apr 16, 2008 10:35 pm; Thanked: 56 times

by raunekk » Tue Feb 10, 2009 9:47 pm

hi uri..
i guess the explanation was perfect...

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vittalgmat: Legendary Member; Posts: 621; Joined: Wed Apr 09, 2008 7:13 pmFollowed by: 4 members; Thanked: 33 times

by vittalgmat » Wed Feb 11, 2009 12:41 am

ontopofit wrote:yes it's correct...besides there is direct formula that number of permutations in circular arr. is (n-1)!.....i.e in this case y=11! and x=12!.hence x=12y.

however, i appreciate the way u have dun it. its better not to depend too much on direct formulas.

Some one pls correct me if I am wrong.
I think ontopofit's approach is incorrect, but since we are looking at a ratio, one can arrive at the same answer as long the same method is used to obtain the value of x and y.
I think Uri's approach is correct.

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