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

Question

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!

chetan2u · Answer

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!

GauravSolanky · Answer

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 :-)

shailendra79s · Answer

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

ehsan090 · Answer

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

0akshay0 · Answer

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.

Bunuel · Answer

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 .

Kinshook · Answer

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

_ankitchawla_ · Answer

I am not able to understand:

To arrange n people in a circular arrangement, total numbers of ways = (n-1)!

so for 6 girls, its 5!

but if there are 6 boys, why is the number of ways 6! and not 5!?

Bunuel · Answer

When you arrange n objects in a circle, the number of arrangements is (n−1)!, because rotating everyone by the same amount does not create a new arrangement. The relative order stays the same.

So for 6 girls, the number of arrangements is 5!.

After the girls are placed, the circle is effectively fixed. The 6 spots for boys are the 6 specific gaps between consecutive girls.

Now the boys are not “in their own circle.” They are being placed into 6 fixed positions relative to the girls. If you shift all the boys by one gap, each boy ends up next to different girls, so it is a different overall seating arrangement.

Therefore, the number of ways to place the 6 boys is 6!, not 5!.

Hope it's clear.

_ankitchawla_ · Answer

Got it now, thanks  Bunuel

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

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

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