The game called Lotto sponsored by the Louisiana Lottery Commission pays its largest prize when a contestant matches all 6...

The game called Lotto sponsored by the Louisiana Lottery Commission pays its largest prize when a contestant matches all 6 of the 44 possible numbers. Assume there are 44 ping-pong balls each with a single number between 1 and 44. Any number appears only once, and the winning balls are selected without replacement.

Use the hypergeometric formula to find the probability of matching all 6 winning numbers. The lottery commission also pays if a contestant matches 4 or 5 of the 6 winning numbers. Hint: Divide the 44 numbers into two groups, winning numbers and nonwinning numbers.

Find the probability, again using the hypergeometric formula, for matching 4 of the 6 winning numbers

Find the probability of matching 5 of the 6 winning numbers.