Name:__________________
Math 7 accel.
Worksheet: Counting Principles
Feb. 9, 2012
1. How many different outcomes are possible if you flip a coin two times? Five times? 𝑛 times?
2. You perform an experiment that consists of rolling a number cube (die) three times.
a. How many possible outcomes are there?
b. What is the probability of rolling a “1” followed by a “2” followed by a “3”?
c. What is the probability that you roll the same number every time?
d. What is the probability that exactly one number is a 6?
e. What is the probability that at least one number is a 6?
3. You have 10 new books that you haven’t read and 12 new music CDs that you haven’t yet listened
to. You’re going on a trip and want to take along some reading and listening material…
a. How many different ways can you select 1 book and 1 CD?
b. How many ways can you select 2 books and 3 CDs?
4. A restaurant claims to have 5040 possible meals that you can create from their menu. A meal
consists of a main course, a salad, a drink, and a dessert. The menu lists 8 main courses and 5 salads.
The drink choices include 7 flavors in 3 sizes. How many dessert choices are there?
5. Give a numerical value for each of the following expressions:
a. 9!
d.
5 𝐶3
b. 8 𝑃4
e.
19 𝑃1
c.
4 𝑃4
f.
35 𝐶33
6. A baseball team has 12 players on the roster, 9 of which are in the lineup for any given game.
a. How many different lineups (sets of 9 players) can be made from the roster of 12 players?
b. Once the lineup has been selected, how many batting orders can be fashioned from the
chosen list of 9 players?
c. How many different batting orders (9 players) can be created from the whole roster of 12
players?
7. You want to design a flag for your club that will have four stripes of different colors. If there are 7
different colors available, how many flags can you create?
8. (continuation) If you get a computer to randomly create your flag, what is the probability that the
flag will have a red stripe? (Red is one of the 7 color choices.)
9. (continuation) What is the probability of having a red stripe if the flag has five(different) stripes?
Six stripes? Seven stripes?
10. How many different 8-song playlists could you create from a CD that has 12 songs on it?
11. You have a drawer with 9 different unmatched socks. If you blindly reach into the drawer and pick
out two socks, how many different sets are possible?
12. If your advisory consists of 12 students, how many ways can you and your fellow advisees be
divided into lunch tables with 6 students at each table?
13. You and five friends go to an amusement park. The Scrambler has cars that only seat four at a time.
How many different groups of four can you and your friends make for this ride?
14. Consider three permutations: 6 𝑃𝑟 7 𝑃𝑟 and
values of 𝑟. Describe any patterns that you see.
8 𝑃𝑟 .
Complete the table below for the indicated
𝑟
6 𝑃𝑟
7 𝑃𝑟
8 𝑃𝑟
1
2
3
4
5
6
7
XXXXX
8
XXXXX
XXXXX
15. Using the patterns you observed in the table in #14, predict which of these has the greatest value:
23 𝑃6
23 𝑃12
23 𝑃18
23 𝑃23
16. Using what you know about combinations, predict which of these has the greatest value:
18 𝐶3
18 𝐶9
18 𝐶17
17. Tell whether the value of 𝑎 𝑃𝑏 is always, sometimes or never greater than the value of
same values of 𝑎 and 𝑏) - explain your reasoning.
𝑎 𝐶𝑏
(for the