I'm really bad with Combinatorics and I can't find similar problems to this one online either. To me, the question isn't very specific which makes it harder for me to find the answer.
A math teacher ordered 13 girls in a class to form a line such that no girl would have girls shorter than her on both sides. All girls in the class are of different height. In how many ways can the girls carry out the teacher's commands?
$\underline {HINT}$
Don't look at the tallest person, fix the shortest person at any of the available positions, and go on placing taller person(s) on adjacent side(s) one by one.
One such possibility for a group of $5$ is depicted pictorially below.
${\Huge...}\quad$Left end
${\Huge ..}$
${\Huge .}\quad$ Shortest person
${\Huge ....}$
${\Huge .....}\quad$Right end
FURTHER HINT
Count the number of possibilities with the shortest person at this position. Do such counts with the shortest person at each available position. Then add up.