CHECK POINT 1 A pizza can be ordered with three choices of size (small, medium, or large), four choices of crust (thin, thick, crispy, or regular), and six choices of toppings (ground beef, sausage, pepperoni, bacon, mushrooms, or onions). How many different one-topping pizzas can be ordered?
CHECK POINT 2 You are taking a multiple-choice test that has six questions. Each of the questions has three answer choices, with one correct answer per question. If you select one of these three choices for each question and leave nothing blank, in how many ways can you answer the questions?
CHECK POINT 3 License plates in a particular state display two letters followed by three numbers, such as AT-887 or BB-013. How many different license plates can be manufactured?
CHECK POINT 4 A corporation has seven members on its board of directors. In how many different ways can it elect a president, vice-president, secretary, and treasurer?
CHECK POINT 5 In how many ways can 6 books be lined up along a shelf?
CHECK POINT 6 For each of the following problems, explain if the problem is one involving permutations or combinations. (It is not necessary to solve the problem.)
a. How many ways can you select 6 free DVDs from a list of 200 DVDs?
b. In a race in which there are 50 runners and no ties, in how many ways can the first three finishers come in?
CHECK POINT 7 From a group of 10 physicians, in how many ways can four people be selected to attend a conference on acupuncture?
CHECK POINT 8 How many different 4-card hands can be dealt from a deck that has 16 different cards?