Problem
COM-B1-M02-P022 Alternating Around a Table
#22
★★★★☆ Level 4 of 5
In how many ways can \(6\) boys and \(6\) girls sit around a round table so that boys and girls alternate?
First seat the boys around the table, then place girls in the gaps.
The boys can be seated around the table in \((6-1)!=120\) ways. This creates \(6\) gaps, into which the \(6\) girls can be placed in \(6!\) ways. Answer: \(120\cdot720=86400\).
Strong problem on gaps and circles.