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In how many ways 5 boys and 6 girls can be seated on 12

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In how many ways 5 boys and 6 girls can be seated on 12 [#permalink] New post 22 Jan 2006, 00:44
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In how many ways 5 boys and 6 girls can be seated on 12 fixed chairs around a fixed circular table, so that no boy is seated adjacent to other boy and no girl is seated adjacent to other girl.
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

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 [#permalink] New post 22 Jan 2006, 05:11
I think the questions says that
1) the arrangements of boys and girls
2) the seats on which they sit are different and have to be counted too( Although it actually doesn't make much difference, because the table is round)

x=boys
_=girls
0=free space

_x_x_x_x_x_0


We see that the free space cannot be betwen a girl and a boy, because otherwise a girl would sit next to another girl.

Fix the free seat, then

1) there are 6!*5!=86400 arrangements

adjust for 2) 6!*5!*12=1036800

Can't imagine that there are so many arrangements, will see what the others get.
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 [#permalink] New post 22 Jan 2006, 05:41
Looks like new GMAT format with Quant section of 3 hours ;)

6G & 5B

1) No. of ways 6 girls can sit on 12 chairs = 12P6
2) No. of ways in which any 2 girls sit together = 12P5

There are 6 chairs left,
3) No. of ways 5 boys can sit on 6 chairs = 6P5

So, total = (12P6 - 12P5) * 6P5 :shock:
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Re: PS - Seating [#permalink] New post 22 Jan 2006, 07:34
b = 5
g = 6
total = 11
total seats = 12

no of ways boys can be seated = 5!
no of ways girls can be seated = 6!
we can only interperse boys in between girls since no girls and no boys can be adjacent.
since there are 12 fixed seats, so 5! 6! arrangements can be done = 12 ways.
so the no of total arrangements = 12 (6!) (5!)
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Re: PS - Seating [#permalink] New post 22 Jan 2006, 15:59
ps_dahiya wrote:
In how many ways 5 boys and 6 girls can be seated on 12 fixed chairs around a fixed circular table, so that no boy is seated adjacent to other boy and no girl is seated adjacent to other girl.


I come up with 6*5!*5!

No. of ways the girls can be seated on the round table with one vacant seat betwn all is (6-1)! = 5!
Now we have 6 vacant seats betn the girls-
select 5 seats out of 6 and arrange the boys=
5C6* 5!

so the no. of ways = 5!5!*6
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 [#permalink] New post 22 Jan 2006, 19:34
I agree with allabout.

12*5!*6!

one empty seat - 12 ways of setting it up.
5 seats for 5 boys. - 5!
6 seats for 6 girls - 6!
  [#permalink] 22 Jan 2006, 19:34
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