Counting, permutations and combinations
Multiply the choices at each stage. If order matters it is a permutation; if not, a combination.
A worked example
Three medals from 8 runners: order matters, so 8P3 = 336. Three delegates from 10: order does not, so 10C3 = 120.
The mistake people actually make
Ask whether swapping two selections gives a different result. If it does not, you need a combination.