Question

please help me find a way to calculate number of ways which 3 girls and 4 boys can be seated on a row of 7 chairs if each arrangement is to be symmetrical. i'm pretty stupid

Answer 1

I reckon there are 3 symmetrical seating arrangements for 3 girls and 4 boys.
If that's the case then each arrangement can have 4! x 3! ways of seating the girls and boys so we have a total of 3 x 4! x 3! ways

Answer 2

For symmetry you should have same number of boys and girls seated towards both side of chair no. 4.. If you make a boy sit on chair no. 4 then you will be left with 3 girls and 3 boys which you cannot divide into two groups of 3 members having same no of boys and girls in each group to be seated on either sides of chair no 4. when you make a girl sit on chair no 4 you will be left with 2 girls and 4 boys which you can divide into two groups containing 1 girl and 2 boys hence having same no of boys and girls,. now you can select the girl to be seated on chair no.4 from three girls in 3 ways....to make 2 groups to be seated on either side of the chair no.4 you can select first boy from 4 boys in 4 ways, second boy from remaining 3 boys in 3 ways and 1 girl from 2 girls in 2 ways, after making 2 groups containing 3 members you can arrange that three members in 3! ways....therefore total no of ways=3x4x3x2x3!=3x4!x3!=432ways..

Answer 3

@Salmon thx

Answer 4

Mention not....Its my pleasure helping you..