/sci/ - Science & Math

>>15380140
Each way to put the flags on the poles can be considered as an ordering of the flags together with a way to split the flags in the poles (see picture).

There are six ways to split five flags in three poles : you can group them 3-1-1 or 2-2-1, and in each case there are three ways to order them.

There are thirty ways to order the five flags : there are 5! permutations, but there are two red and two blue flags, so the number of possibilities is [math]\frac{5!}{2!2!} = 30[/math].

So the final number of possibilites is 6*30 = 180.