1) A legislative committee consists of 13 democrats, 7 republicans, and 3 independents. A delegation of 3 is selected to attend an environmental summit.
a) How many different delegations are possible?
b) How many different delegations consist of at least 1 republican?
2) 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 the 1973 Kentucky Derby a total of 13 horses raced and if a person decided to make a bet on the race:
a) How many different possible trifecta bets coulc they have made?
b) How many different possible boxed trifect bets could they have made?
3) In how many ways can the letters in the word LEPIDOPTEROLOGY be arranged?