Seating five boys and five girls alternately

A teacher brings $5$ boys and $5$ girls to a show, and they sit in a single row of $10$ seats. The rule is that neighbours must always be of opposite genders. How many seating arrangements satisfy this rule?

28,800. The genders must alternate, so either the boys take the odd seats or the even seats ($2$ patterns). Within a pattern the boys can be ordered in $5!$ ways and the girls in $5!$ ways, giving $2\cdot(5!)^2=28{,}800$.