Question: In each day that the Mass Cash lottery is run in Massachusetts, 5 of the integers from 1 to 35 are chosen (randomly and without replacement).
(a) When playing this lottery, find the probability of guessing exactly 3 numbers right, given that you guess at least 1 of the numbers right.
(b) Find an exact expression for the expected number of days needed so that all of the 35 5 possible lottery outcomes will have occurred.
(c) Approximate the probability that after 50 days of the lottery, every number from 1 to 35 has been picked at least once.