a box contains 10 chocolate chip cookies 8 sugar cookies and 2 oatmeal raisin cookies. if harry randomly selects 3 cookies without replacement what is the probability they are different flavors?

Rephrased, what is the chance that he chooses one of each kind of cookie? Well, this can happen in one of several ways. We sum probabilities over the ways:

Chooses chocolate, then sugar, then oatmeal: 10/20x8/19x2/18 ; chocolate, oatmeal, sugar: 1/20x2/19x8/18