1) In horse racing, a trifecta bet is one where you need to pick the first three finishers of the race in the exact order in order to win the bet and a boxed trifecta bet is one where you need to pick the first three finishers in the race in any order to win. In this year’s (2015) Kentucky Derby a total of 18 horses raced and if a person decided to make a bet on the race:
a) How many different possible trifecta bets could they have made?
b) How many different possible boxed trifecta bets could they have made?
2) Suppose that an unfair coin comes up heads 53.2% of the time. The coin is flipped a total of 19 times.
a) What is the probability that you get exactly 11 tails?
b) What is the probability that you get at most 17 heads?