Have the 55 boys stand in a line. This can be done in 5!5! ways. For the moment, add a boy at each end, who will be removed when we're done. Now send the 33 girls, one at a time, to stand between two boys. The first girl has 66 choices, the second girl will have 55 choices, and the third girl will have 44 choices. This gives a total of 5!⋅6⋅5⋅4=14,4005!⋅6⋅5⋅4=14,400 arrangements. Remove the two extra boys, and have the others sit. Remark: the fiction of the extra two boys is simply to avoid having to elaborate that each girl can either wedge herself between two boys or else stand next to a boy at one end or the other.