A state runs a lottery in which six numbers are randomly selected from 40, without replacement. A player chooses six numbers before the state's sample is selected.
(a) What is the probability that the six numbers chosen by a player match all six numbers in the state's sample?
(b) What is the probability that ?ve of the six numbers chosen by a player appear in the state's sample?
(c) What is the probability that four of the six numbers chosen by a player appear in the state's sample?
(d) If a player enters one lottery each week, what is the expected number of weeks until a player matches all six numbers in the state's sample?