BdMO Online Forum

Problem 9:
At a convention, flags of $4$ countries are to be hoisted on $2$ poles so that no pole is left empty and all the flags get hoisted. More than one flag must not be placed at the same height of the same pole. Rather, they can be placed above or below an already placed flag. In this manner, more than one flag can be placed serially on a single pole. How many ways can the flags be hoisted?

the possible cases are 2 flags o each pole,3 on first and3 on 2nd.
in each of the cases the flags can be hoisted in $4!$ ways. so the ans is $4!*3=72$