1. A horse race has 14 horses entered. You have foolishly decided to place a trifecta bet, in which you must predict the first three finishers in the race. Assuming that each horse is equally likely to finish in each place (a dubious assumption, but for now that's okay!), what is the probability that you pick the correct top three finishers? (Recall the classical approach to probability.)
2. A national association is planning its next annual conference. There are 44 cities in the country from which to choose, and the committee has decided to select five cities randomly from the list of 44 in order to present the list to a larger group for consideration. How many different lists of five cities are possible?
3. During training for firefighters, an instructor decides to test the firefighters by randomly selecting a firefighter for each of five tasks. There are twelve firefighters altogether, and a firefighter may be selected for more than one task. How many different ways might the instructor choose the five firefighters?