17. A fair die is tossed successively. Let X denote the number of tosses until each of the six possible outcomes occurs at least once. Find the probability mass function of X.

Hint: For 1 ≤ i ≤ 6, let Ei be the event that the outcome i does not occur during the first n tosses of the die. First calculate P(X > n) by writing the event X > n in terms of E1, E2, . . . , E6.