MATH 182, MATHEMATICAL ANALYSIS II Exam

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(d) 10P6 (e) 6C4 (f) 9P3

2. If there are 5 ways to travel from town A to town B, 7 ways to travel from town B to town C, and 3 ways to travel from town C to town D, how many different ways are there to travel from town A to town D?

3. If an ice cream parlor has 14 different flavors of ice cream, 6 different toppings, and 4 different styles of cones, how many different varieties of ice cream cones are available to the customer?

4. The Postal Service is encouraging the use of 9-digit zip codes in most areas. How many zip codes are possible

(a) if there are no restrictions on the digits used?

(b) if only odd numbers can be used?

(c) if the first number cannot be zero and the last must be 9?

5. How many different 6-letter radio station call letters can be made

(a) if the first letter must be K, and letters may not be repeated?

(b) if the first letter must be K, the fourth letter must be Z, and letters may not be repeated?

(c) if repeats are allowed (but the first letter is K or and the fourth letter is Z)?

6. How many 8-member committees can be formed from a class consisting of 25 students? What if two particular students must be included on the committee?

7. In a game of musical chairs, 11 children will sit in 8 chairs arranged in a row. Three children will be left out. In how many ways can the 11 children find seats?

8. A mailman has special delivery mail for 9 customers.

(a) In how many ways can he arrange his schedule to deliver to all 9?

(b) In how many ways can he schedule deliveries if he can deliver to only 7 of the 9?

9. Seven orchids are to be selected from a collection of 12 for a flower show.

(a) In how many ways can this be done?

(b) In how many different ways can the group of 7 be selected if 4 particular orchids must be included?

10. A jar contains 4 yellow, 3 orange, and 7 red jelly beans. Three jelly beans are selected at random. Find the probability that the selection includes the following.

(a) All orange jelly beans (b) 3 yellow and 2 red jelly beans

(c) At most 1 yellow jelly bean (d) At least 2 red jelly beans

11. Five cards are drawn at random from an ordinary deck of 52 cards. Find the probability that the 5-card hand contains the following:

(a) 3 kings and 2 queens (b) No diamonds

(c) 3 cards of the same suit (d) At least 3 aces

12. A die is rolled 6 times. Find the probability of rolling

(a) Exactly 4 twos (b) Exactly 5 threes (c) At most 3 fours

13. A coin is tossed 7 times. Find the probability of rolling

(a) All tails (b) At most 4 tails (c) Exactly 3 heads

14. Eighty-one percent of all students at a certain school ski. If a sample of 35 students at this school is selected, and if their responses are independent, find the probability that exactly

(a) 22 of the 35 students ski (b) All 35 students ski