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# In how many ways can be 6 boys and 6 girls sit around circular table

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Math Expert
Joined: 02 Sep 2009
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In how many ways can be 6 boys and 6 girls sit around circular table  [#permalink]

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22 Jan 2015, 07:52
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5
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Difficulty:

65% (hard)

Question Stats:

48% (01:11) correct 52% (01:33) wrong based on 161 sessions

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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!

Kudos for a correct solution.

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Posts: 6975
Re: In how many ways can be 6 boys and 6 girls sit around circular table  [#permalink]

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23 Jan 2015, 10:27
1
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]

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07 Sep 2015, 21:30
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]

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07 Sep 2015, 22:10
1
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!
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Re: In how many ways can be 6 boys and 6 girls sit around circular table  [#permalink]

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27 Mar 2017, 23:16
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
TIA
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Re: In how many ways can be 6 boys and 6 girls sit around circular table  [#permalink]

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27 Mar 2017, 23:27
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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Posts: 50009
Re: In how many ways can be 6 boys and 6 girls sit around circular table  [#permalink]

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27 Mar 2017, 23:47
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 &nbs [#permalink] 27 Mar 2017, 23:47
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# In how many ways can be 6 boys and 6 girls sit around circular table

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