One semester in a chemistry class, 14 students failed due to a poor attendance, 24 failed due to not studying, 14 failed because they did not turn in assignments, 8 failed because of poor attendance and not studying, 7 failed because of not studying and not turning in assignments, 4 failed because of poor attendance and not turning in assignments, and 2 failed because of all three of these reasons. (a) How many failed for exactly two of the three reasons?

In how many ways can 5 people stand in a line if one person demands to be first?

A hospital cafeteria offers a fixed-price lunch consisting of a main course, a dessert, and a drink. If there are four main courses, three desserts, and six drinks to pick from, in how many ways can a customer select a meal consisting of one choice from each category?

How many different signals can be sent, when three flags are used, if two of the 9 flags are missing?