Problem
COM-B1-M02-P013 Girls Not Adjacent
#13
★★★☆☆ Level 3 of 5
In how many ways can \(5\) boys and \(4\) girls stand in a row so that no two girls are adjacent?
First arrange the boys, then choose gaps for the girls.
The boys can be arranged in \(5!\) ways. Around them are \(6\) gaps: before the first, between neighbors, and after the last. Choose \(4\) gaps for the girls and arrange the girls in \(4!\) ways. Answer: \(5!\cdot15\cdot4!=43200\).
Key gap method.