The game called Lotto sponsored by the Louisiana Lottery

The game called Lotto sponsored by the Louisiana Lottery Commission pays its largest prize when a contestant matches all 4 of the 29 possible numbers. Assume there are 29 ping-pong balls each with a single number between 1 and 29. Any number appears only once, and the winning balls are selected without replacement.

a. The commission reports that the probability of matching all the numbers are 1 in 23,751. What is this in terms of probability? (Round your answer to 8 decimal places.)

b. Use the hypergeometric formula to find the probability of matching all 4 winning numbers. The lottery commission also pays if a contestant matches 2 or 3 of the 4 winning numbers. Divide the 29 numbers into two groups, winning numbers and nonwinning numbers. (Round your answer to 8 decimal places.)

c. Find the probability, again using the hypergeometric formula, for matching 2 of the 4 winning numbers. (Round your answer to 8 decimal places.) 

d. Find the probability of matching 3 of the 4 winning numbers. (Round your answer to 8 decimal places.)