Assignment:
A state runs a lottery in which 6 numbers are randomly selected from 40, 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 the player match all 6 numbers in the state's sample?
b. What is the probability that 5 of the 6 numbers chosen by the player match all 6 numbers in the state's sample?
c. What is the probability that 4 of the 6 numbers chosen by the player match all 6 numbers in the state's sample?
d. If the 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?
Provide complete and step by step solution for the question and show calculations and use formulas.