I think the counting principle is the simplest. Say you have 4 sandwiches and 2 drinks. How many different lunches can you make. 4 x 2 = 8. It's multiplicative.
Combination and permutations are how to arrange things. Going along with food again, say you have 4 different pies and was going to eat 3 of them. How many ways can you eat them. If the order in which you eat them is important, then it's permutation. If not, then it's combination.
