Originally Posted by kodirl
There can be five possible places in table where each girl can seat:
1 d 2 e 3 f 4 g 5 h
Totally possible combinations of a,b,c are 3*2*1 = 6 so there can be totally 6 arrangements of girls in 5 places.
Since each arrangement of girls (for example a,b,c) can be arranged in table in totally 9 combinations around table so that no two girls are together then its totally 6*9 = 45 combinations of girls around table.
Now there can be 5*4*3*2*1 = 120 combinations of boys arrangement.
Multiply total combinations of boys and girls 120*45 and you get that is totally 5400 arrangements if no two girls are siting together.