How many distinct arrangements of four letters (without repeats) from the set {a, b, c, d, e} are possible? 15?

From the pool of 5 letters, we're picking 4. We can arrange the 4 we picked in ways.

But there are 5 ways of *not* picking the remaining letter. To account for the arrangements containing the letter not picked, we multiply this total by 5.

Put another way, suppose we drew a, b, c, and d, but not e. We have 24 possible arrangements for these 4 letters, but for any distinct arrangement there are 5 ways of replacing any letter with e.

So the number of arrangements we can actually make is .

The answer would be 27 because assuming that each package has 1 bar of soap and 1 tube of toothpaste, after 27 packages they would run out of toothpaste