1) An ice cream store sells two drinks (sodas or milk shakes), in four sizes (small, medium, large, or jumbo), and five flavors (vanilla, strawberry, chocolate, coffee, or pistachio). In how many ways can a customer order a drink? My Answer: 2*4*5 = 40 ways to order drink.
2) There are 12 standbys who hope to get seats on a flight, but only 5 seats are available on the plane. How many different groups of 5 people can be selected for the flight? My Answer: 12_C_5 = 12!/ (12-5)! 5! = 792 different groups of people selected for flight.
3a) The physics dept. schedules four lecture sectiosn and fifteen laboratory sections for its freshman course. In how many different ways can a student choose one of each? My Answer: 4*15 = 60 ways - because both are 2 different events.
3b) How many choices are left if two of the lecture sections and four of the laboratory sections are full by the time the student gets to enroll? My Answer: (using the same logic on 3a) 2*11 = 22 choices remaining.
Please correct me where I'm wrong & explain if you have time.