#2**0 **

a) \(10! \) ways to arrange the boys and \(8!\) ways to order the girls. There are also 2 ways to order the groups (10 boys, 8 girls; 8 girls, 10 boys).

This makes for \(8! \times 10! \times 2 = \color{brown}\boxed{292,626,432,000}\) ways.

b) \(8! \) ways to order the girls. Now, treat the 8 girls as 1 person. Now, there are \(11!\) ways to order everything else.

This makes for \(8! \times 11! = \color{brown}\boxed{1,609,445,376,000} \) ways.

BuilderBoi Jun 19, 2022