CP Algebra 2
Counting and Probability Review
Name_________________________
4/11/13
1. What is the difference between a permutation and a combination?
2. Complete the table of CHS students’
favorite extra-curricular.
sports
Sophomore 140
Perforimg
arts
50
Junior
50
150
Use the chart to determine the
probability.
a. P(junior)
Total
b. P(performing arts)
c. P(sophomore or performing arts)
d. P(junior and sports)
Total
e. P(junior|sports)
3. When you open a rotating lock, order is _________________ (important or not important),
so this is a ___________________________ (permutation or combination).
4. Katie wants to adopt kittens from a litter of 11. In how many ways can she choose 3
kittens?
5. Write a problem for...
a. 20 P3

b.

72
C11
6. Two solutions to “How many Internet codes can be made by using 3 digits if 0 is
excluded and digits may not be repeated?” Who is correct? Explain!
Student A
Student B
9!
3!(9 - 3)!
9!
(9  3)!

7. A paper clip holder has 100 paper clips: 30 are red, 25 are yellow, 15 are pink, 11 are blue,
and 19 are green.
a. A paper clip is randomly chosen. What is the probability that the paper clip is
yellow?
b. A paper clip is randomly chosen. What is the probability that the paper clip is
NOT green?
c. Two paper clips are chosen WITH replacement. What is the probability that the
first paper clip is red and the second paper clip is pink?
d. Two paper clips are chosen one at a time WITHOUT replacement. What is the
probability that both paper clips are green?
e. Three paper clips are chosen one at a time WITHOUT replacement. What is the
probability that you choose 1 red, then 1 yellow, and finally 1 green?
f. Two paper clips are chosen one at a time WITHOUT replacement. Find P(1 blue
AND 1 red).
g. Two paper clips are chosen one at a time WITH replacement. Find
red).
P(2 blue OR 2
8. How many ways can a jury of 12 and 2 alternate jurors be selected from 30 potential
jurors?
9. A hiker can take 4 trails to the lake and then 3 trails from the lake to the cabins. How
many routes are there from the lake to the cabins?
10. There are six cars entered in a particular race. In how many different ways can four of
them finish first, second, third, and fourth?
11. State Farm Insurance Company received ten claims for car accidents during one week.
Management decides to select three of these claims randomly and to investigate them
thoroughly. In how many different ways can this be done?
13.
Each of the 8 questions on a multiple-choice
test has 4 possible answers. If all the questions are answered, in how many ways can the
test be completed?
14. Katie’s art store makes custom paints using a base, a texture, and a pigment. If the store
has 3 different bases, 2 textures, and 18 pigments, how many different custom paints can
be mixed?
15. There are 10 pennies, 8 nickels, and 5 dimes in a bank.
a. You are selecting 4 coins with replacement. Find P(all pennies).
b. You are selecting 4 coins with replacement. Find P(all quarters).
16. One card is chosen at random from a deck of 52 playing. Calculate the following
probabilities.
a. P(8 or a heart)
b. P(Queen or a King)
c. P(Ace or a red card)
17. Two cards are chosen at random from a deck of 52 playing. Calculate the following
probabilities.
a. P(King then a heart) WITH replacement
b. P(King then a King) WITH replacement
c. P(King then a King) WITHOUT replacement
18. Student Government consists of 28 members, 16 males and 12 females.
a. Four members are chosen to be directors. How many different 4-person groups of
directors are possible?
b. If the group of directors must be two males and two females, how many different 4person groups of directors are possible?
c. Suppose that STUGO decides instead to select ranked officers. If a President, VicePresident, Secretary, and a Treasurer are chosen as officers, how many different
outcomes are possible?
d. Suppose that STUGO decides to select only a President and Vice-President and they must
be of different genders. How many different outcomes are possible?