10 Jul math 182
. Evaluate the following factorials, permutations, and combinations.
(a) 8! (b)
3
!
7
(c)
÷
ø
ö
ç
ç
è
æ
4
6
(d) 11P9 (e) 4C2 (f) P(10,7)
2. If an ice cream parlor has 21 different flavors of ice cream, 4 different styles of cones, and 6 different toppings, how many different varieties of ice cream cones are available to the customer?
3. A collection of 7 paintings by one artist and 6 by another is to be displayed.
(a) In how many ways can the paintings be displayed in a row?
(b) In how many ways can the paintings be displayed if the works of the artists are be alternated?
(c) In how many ways can the paintings be displayed if the works by each artist are grouped together?
4. The Postal Service is encouraging the use of 9-digit zip codes in most areas. How many zip codes are possible
(a) if only odd numbers can be used?
(b) the first number cannot be zero and there are no other restrictions?
(c) if the first number must be one and the last number must be nine and there are no other restrictions?
5. A license plate consists of 3 letters followed by 3 numbers. How many different license plates can be made
(a) if there are no restrictions and the letters and numbers can be repeated?
(b) if there are no restrictions and the letters and numbers cannot be repeated?
(c) if the first two letters must be an A and B and the letters and numbers can be repeated?
6. An office manager must select 9 employees from a total of 12 to work on a project.
(a) In how many ways can he select the group of 9?
(b) In how many ways can he select the group of 9 if two particular employees must be selected?
7. In a game of musical chairs, 12 children will sit in 11 chairs arranged in a row. One child will be left out. In how many ways can the 12 children find seats?
8. A mailman has special delivery mail for 13 customers.
(a) In how many ways can he arrange his schedule to deliver to all 13?
(b) In how many ways can he schedule deliveries if he can deliver to only 10 of the 13?
9. Seven orchids are to be selected from a collection of 9 for a flower show.
(a) In how many ways can this be done?
(b) In how many different ways can the group of 6 be selected if 1 particular orchid must be included?
10. A jar contains 5 yellow, 7 orange, and 6 red jelly beans. Four jelly beans are selected at random. Find the probability that the selection includes the following.
(a) All red jelly beans (b) 2 yellow and 1 orange jelly bean
(c) No yellow jelly beans (d) At most 2 orange 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) 2 kings and 3 queens (b) All hearts
(c) 2 cards of the same suit (d) At most 2 clubs
12. A coin is tossed 6 times. Find the probability of rolling
(a) No heads (b) At least 3 tails (c) Exactly 2 heads
13. A die is rolled 9 times. Find the probability of rolling
(a) Exactly 3 fours (b) All sixes (c) No more than 4 ones
14. Suppose that 19 percent of the jet engines manufactured in a certain way are defective. Assuming independence, find the probability of getting each result in a sample of 7 jet engines.
(a) 5 defective jet engines (b) At least 5 defective jet engines
(c) At most 5 defective jet engines
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