I am currently taking a course in Calculus, and a course in Probability/Statistics at my local University. Probability has always been my weak spot in math, so I might post questions here from time to time. Especially since we are stuck with "Probability and Statistical Inference" by Hogg and Tanis as our textbook. This book has no student solution's manual, so it can be a very frustrating book to work with.

Anyway, here goes:

There are three teams in a cross-country race. Team A has five runners, team B has six runners, and team C has seven runners. In how many ways can the runners cross the finish line if we are interested only in the team for which they run? That is, what is the number of distinguishable permutations of five A's, six B's, and seven C's? (Note that, for scoring purposes, only the scores of the five first runners for each team count.)

Any tips on solving this problem will be greatly, greatly appreciated!