5 girls and 4 boys are seated in a row. Calculate the number of ways this can be done if: a)the girls sit together and the boys sit together b) Adam and Betty are not allowed to sit next to each other

Question

Answers:

a) 5760

b) 282240

Answer 1

a) 5!4!x2= 5x4x3x2x1x4x3x2x1x2 =120x24x2=5760

it's 5!4! times 2, as there's two ways to have each gender sit together,

either BBBBBGGGG or GGGGBBBBB

b) if there are no limits on how they sit, the total ways are 9!8!7!6!5!4!3!2!1!

then subtract from that when Adam is next to Betty