Find the number of ways in which 3girls &4boys can be seatedin apow of 7 chairs if each arrangement is to be?

Question

symmetrical

Answer 1

bgbgbgb
bbgggbb
gbbgbbg

3

Answer 2

Well, the question is what is meant by "symmetrical"? E.g., does it mean that there's a boy in the 1st chair if and only if there's a boy in the 7th chair?

In that case, the answer goes like this.

There are three possibilities -- boys in chairs 1, 2, 6, 7; boys in chairs 1, 3, 5, 7; and boys in chairs 2, 3, 5, 6.

For each of those possibilities, there are 4! = 24 ways to arrange the boys and 3! = 6 ways to arrange the girls.

So the answer is 3 * 24 * 6 = 432.

Answer 3

Hi there. :)

Unfortunately, I don't remember the proper formula(which is the easiest way to get the answer). So I had to do this the long and hard way. There are 35 arrangements in all, as follows:

b b b b g g g------b b b g b g g------b b b g g b g------b b b g g g b


b b g b b g g------b b g b g b g------b b g b g g b------b b g g b b g


b b g g b g b------b b g g g b b------b g b b b g g------b g b b g b g


b g b b g g b------b g b g b b g------b g b g b g b------b g b g g b b


b g g b b b g------b g g b b g b------b g g b g b b------b g g g b b b


g b b b b g g------g b b b g b g------g b b b g g b------g b b g b b g


g b b g b g b------g b b g g b b------g b g b b b g------g b g b b g b,


g b g b g b b------g b g g b b b------g g b b b b g------g g b b b g b,


g g b b g b b------g g b g b b b------g g g b b b b


I hope this helps. :) Good luck. :)

Answer 4

You need an equal number of girls on each side of the middle, same for boys. So excluding the middle seat we need an even number of each sex. Ergo, a girl must be in the middle, leaving 2 boys and 1 girl on each side.

Possible patterns:
BBGGGBB
BGBGBGB
GBBGBBG

For each of these patterns, there are 4! ways to seat the boys and 3! ways to seat the girls, so in total we have

3 patterns x 4! boy arrangements x 3! girl arrangements
= 3 x 24 x 6
= 432 arrangements.