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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 five 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 playermatches all six numbers in the state’s sample?