I'm confused between the difference in permutation and combination, and I'm confused what *n* and *r* stand for.

Combinations are just that: different ways of combining options. Permutations are combinations where the order matters.

If you have ten ingredients have you have to toss six of them into a pot all at once, you would be doing "ten, choose six", because the order in which you toss them doesn't matter. You need only pick the combination of six ingredients.

On the other hand, suppose you're doing a science experiment where you put six of ten chemicals into a beaker, and the order in which the chemicals are added affects the results. You would then be doing "ten, permute six", because the order in which you toss them is

*does* matter.

The variables "n" and "r" correspond to the "ten" and the "six" in the examples above.

Note: The exercises you have posted imply that you are expected to be familiar with the above terminology, along with the related concepts and formulas, and also with more-advanced material.

Eliz.