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how to solve these I am perplexed. Thanks in advance.

 Jun 19, 2022
 #1
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is it 10!*8!*2 = 292,626,432,000

 Jun 19, 2022
 #2
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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.

 Jun 19, 2022
 #3
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thanks

Guest Jun 19, 2022

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