"Combinations" gives the number of ways a subset of r items can be chosen out of a set of n items. "Permutations" makes the same calculation, but in this case different arrangements of the same items are also counted.
For example, for a deck of cards n=52. There are 22100 ways that 3 cards can be chosen (nCr when r=3), but 132600 ways if it matters what order they are drawn in (nPr when r=3).