Assume that in a lottery, 20 balls numbered 1 to 20 are put in a large bowl and then 3 balls are selected, one after the other, at random and without replacement. What is the probability that the third ball drawn has the largest number on it?

(Hint: Let E be the event that the third ball has the largest number, and Bi be the event that the maximum of the first two numbers is equal to i for 1 ≤ i ≤ 20. Find the probabilities P(Bi) for each i and apply the law of the total probability.)