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In how many ways can be 6 boys and 6 girls sit around circular table
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Bunuel
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In how many ways can be 6 boys and 6 girls sit around circular table [#permalink] New post  22 Jan 2015, 06:52
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In how many ways can be 6 boys and 6 girls sit around circular table so that no two boys sit next to each other?

A. (5!)^2
B. (6!)^2
C. 5!6!
D. 11!
E. (5!)^2*6!

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chetan2u
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Re: In how many ways can be 6 boys and 6 girls sit around circular table [#permalink] New post  23 Jan 2015, 09:27
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ANS C..
first fix one boy and place other 5 in alt seats so total ways is 5!
now place each girl between a pair of boys... total ways of seating arrangement of girls 6!
total is 5!*6!
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Re: In how many ways can be 6 boys and 6 girls sit around circular table [#permalink] New post  07 Sep 2015, 20:30
Hi Bunuel,

Can we have the OA please. IMO, it should be C.

no.of arrangements for girls= (6-1)!= 5!
This will give 6 empty spaces for 6 boys. Hence, we can arrange them in 6! ways.

c) 5!*6!


Thanks,
Gaurav :-)
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Re: In how many ways can be 6 boys and 6 girls sit around circular table [#permalink] New post  07 Sep 2015, 21:10
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No. of ways in which girls can be seated after fixing a seat on the circular table = (6-1)! = 5!
No. of ways in which boys can be seated on the vacant seats = 6!
Total no. of ways = 5!x6!
Answer: C
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Re: In how many ways can be 6 boys and 6 girls sit around circular table [#permalink] New post  27 Mar 2017, 22:16
GauravSolanky wrote:
Hi Bunuel,

Can we have the OA please. IMO, it should be C.

no.of arrangements for girls= (6-1)!= 5!
This will give 6 empty spaces for 6 boys. Hence, we can arrange them in 6! ways.

c) 5!*6!


Thanks,
Gaurav :-)


Hi explain a little...
why we are subtracting 1 from girls
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Re: In how many ways can be 6 boys and 6 girls sit around circular table [#permalink] New post  27 Mar 2017, 22:27
ehsan090 wrote:
GauravSolanky wrote:
Hi Bunuel,

Can we have the OA please. IMO, it should be C.

no.of arrangements for girls= (6-1)!= 5!
This will give 6 empty spaces for 6 boys. Hence, we can arrange them in 6! ways.

c) 5!*6!


Thanks,
Gaurav :-)


Hi explain a little...
why we are subtracting 1 from girls
TIA


To find the no.of arrangements in a circular fashion we always use the formula (n-1)! where n is the total number of entities.
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Bunuel
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Re: In how many ways can be 6 boys and 6 girls sit around circular table [#permalink] New post  27 Mar 2017, 22:47
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ehsan090 wrote:
GauravSolanky wrote:
Hi Bunuel,

Can we have the OA please. IMO, it should be C.

no.of arrangements for girls= (6-1)!= 5!
This will give 6 empty spaces for 6 boys. Hence, we can arrange them in 6! ways.

c) 5!*6!


Thanks,
Gaurav :-)


Hi explain a little...
why we are subtracting 1 from girls
TIA


The number of arrangements of n distinct objects in a row is given by \(n!\).
The number of arrangements of n distinct objects in a circle is given by \((n-1)!\).

The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:

\(\frac{n!}{n} = (n-1)!\).

Check other Arrangements in a Row and around a Table questions in our Special Questions Directory.
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Re: In how many ways can be 6 boys and 6 girls sit around circular table [#permalink] New post  01 Feb 2020, 08:19
Bunuel, why dont we multiply 5!6! by 2 considering that we can interchange the positions of the boys and girls?
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Re: In how many ways can be 6 boys and 6 girls sit around circular table [#permalink]
01 Feb 2020, 08:19
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