It is not uncommon after a round of golf to find a foursome in the clubhouse shaking the bar dice to see who buys the refreshments. In the first two rounds, each person gets to shake the five dice once. The person with the most dice with the highest number is eliminated from the competition to see who pays. So, for instance, four 3s beats three 5s, but four 6s beats four 3s. The 1s on the dice are wild, that is, they can be used as any number.
a. What is the probability of getting five 6s? (Remember 1s are wild.)
b. What is the probability of getting no 6s and no 1s?