1. A catered menu is to include a soup, a main course, a dessert, and a beverage. Suppose a customer can select from four soups, five main courses, three desserts, and two beverages. How many different menus can be selected?

2. Find the number of different permutations of the letters in the word GROUP.

3. Find the number of distinguishable permutations of the letters in ASSOCIATIVE.

4. At a certain college, the housing office has decided to appoint, for each floor, one male and one female residential advisor. How many different pairs of advisors can be selected for a seven-story building from 12 male candidates and 15 female candidates?

5. In how many ways can five balls be chosen so that

(a)   all five are red?

(b)   all five are black?

6. (a )  The sum of the numbers is less than 7.

(b)   The sum of the numbers is greater than 8.

7. (a) What is the probability of correctly guessing a person’s four-digit PIN?

(b)   People often use the four digits of their birthday (MM-DD) to create a PIN. What is the probability of correctly guessing a PIN created this way, if the birthday is known?