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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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GauravSolanky
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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GauravSolanky
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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ehsan090
GauravSolanky
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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Asked: 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?

Number of ways to seat 6 girls = 5!
Number of ways to seat 6 boys in vacant seats = 6!
Number of ways can be 6 boys and 6 girls sit around circular table so that no two boys sit next to each other 5!*6!

IMO C
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