A state runs a lottery in which 6 numbers are randomly selected from 42, without replacement. A player chooses 6 numbers before the state's sample is selected. (a) What is the probability that the 6 numbers chosen by a player match all 6 numbers in the state's sample? (b) What is the probability that 5 of the 6 numbers chosen by a player appear in the state's sample? (c) What is the probability that 4 of the 6 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 6 numbers in the state's sample?

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