Question: 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

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 ex- pected number of weeks until a player matches all six numbers in the state's sample?

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