Suppose a fair die is tossed three times. Let X be the number of different faces that appear (so X = 1, 2, 3). Find px(k).
There are $\displaystyle 6^3$ possible outcomes.
There are $\displaystyle 120$ ways to have three different faces.
There are $\displaystyle 90$ ways to have two different faces.
There are $\displaystyle 6$ ways to have only one face.