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# Prealgebra

## Educators

### Problem 1

Tell whether each situation is a permutation or combination.
How many ways can 5 people be arranged in a line?

Ashley V.

### Problem 2

Tell whether each situation is a permutation or combination.
How many programs of 4 musical pieces can be made from 8 possible pieces?

Ashley V.

### Problem 3

Tell whether each situation is a permutation or combination.
How many ways can a 3 -player team be chosen from 9 students?

Ashley V.

### Problem 4

Tell whether each situation is a permutation or combination.
How many ways can 6 different flowers be chosen from 12 different flowers?

Ashley V.

### Problem 5

A pizza shop has 12 toppings from which to choose. If 3 toppings are chosen randomly for a pizza, what is the probability that it is topped with pepperoni, onion, and sausage?

Ashley V.

### Problem 6

Tell whether each situation is a permutation or combination.
How many ways can 6 cars line up for a race?

Ashley V.

### Problem 7

Tell whether each situation is a permutation or combination.
How many different flags can be made from the colors red, blue, green, and white if each flag has three vertical stripes?

Ashley V.

### Problem 8

Tell whether each situation is a permutation or combination.
How many ways can 4 shirts be chosen from 10 shirts to take on a trip?

Ashley V.

### Problem 9

Tell whether each situation is a permutation or combination.
How many ways can you buy 2 DVDs from a display of $15 ?$

Ashley V.

### Problem 10

Tell whether each situation is a permutation or combination.
How many 3-digit numbers can you write using the digits $6,7,$ and 8 exactly once in each number?

Ashley V.

### Problem 11

Tell whether each situation is a permutation or combination.
There are 12 paintings in a show. How many ways can the paintings take first, second, and third place?

Ashley V.

### Problem 12

Tell whether each situation is a permutation or combination.
How many 5 -card hands can be dealt from a standard deck of 52 cards?

Ashley V.

### Problem 13

Tell whether each situation is a permutation or combination.
How many ways can you choose 3 flavors of ice cream from a choice of 14 flavors?

Ashley V.

### Problem 14

Tell whether each situation is a permutation or combination.
Twelve points are marked on a circle. How many different line segments can be drawn between any two of the points?

Ashley V.

### Problem 15

Tell whether each situation is a permutation or combination.
Nine people gather for a meeting. Each person shakes hands with every other person exactly once. How many handshakes will take place?

Ashley V.

### Problem 16

Use the information at the left.
FIGURE CAN'T COPY
Suppose you only have time to ride eight of the coasters. How many ways are there to ride eight coasters if order is important?

Ashley V.

### Problem 17

Use the information at the left.
FIGURE CAN'T COPY
How many ways are there to ride eight of the coasters if order is not important?

Ashley V.

### Problem 18

Use the information at the left.
FIGURE CAN'T COPY
What is the probability that the first two of the eight coasters you ride are the Millennium Force and the Top Thrill Dragster? Suppose you chose to ride the two coasters at random.

Ashley V.

### Problem 19

In a best-of-three series, the first team to win 2 games wins the series. Two ways to win a best-of-three series are to win the first 2 games or lose the first game and win the next two games. How many ways are there to win a best-of-three series? a best-of-five series? a best-of-seven series?

Ashley V.

### Problem 20

Use the following information. Three roses are to be placed in a vase. The color choices are red, pink, white, yellow, and orange.
How many different 3 -rose combinations can be made from the 5 roses?

Ashley V.

### Problem 21

Use the following information. Three roses are to be placed in a vase. The color choices are red, pink, white, yellow, and orange.
What is the probability that 3 roses selected at random will include pink, white, and yellow?

Ashley V.

### Problem 22

Use the following information. Three roses are to be placed in a vase. The color choices are red, pink, white, yellow, and orange.
What is the probability that 3 roses selected at random will not include red?

Ashley V.

### Problem 23

Suppose your cell phone uses a 4-digit personal identification number (PIN) to lock it from use.
How many PINs can you choose to lock your cell phone?

Ashley V.

### Problem 24

Suppose your cell phone uses a 4-digit personal identification number (PIN) to lock it from use.
Use probability to explain how someone is unlikely to guess your PIN.

Ashley V.

### Problem 25

Sindu thinks choosing five CDs from a collection of 30 to take to a party is a permutation. Amanda thinks it is a combination. Who is correct? Explain your reasoning.

Ashley V.

### Problem 26

Write a problem that can be solved by finding $P(4,3).$

Ashley V.

### Problem 27

Is the value of $P(x, y)$ sometimes, always, or never greater than the value of $C(x, y) ?$ (Assume $x \neq 1, y \neq 1$, and $x \neq y$.)

Ashley V.

### Problem 28

Determine whether the following statement is always true. If it is not, provide a counterexample.

Ashley V.

### Problem 29

Writing in Math Why is order sometimes important when determining outcomes? Give an example of a situation where order is important and one where order is not important.

Check back soon!

### Problem 30

When the Rockets win a basketball game, the 12 players on the team give each other high-fives. How many distinct high-fives are given?
A 24
B 36
C 66
D D96

Ashley V.

### Problem 31

How many different slates of officers could be made if a slate consists of one candidate for each office?
$$\begin{array}{|c|c|c|} \hline \text { President } & \text { Secretary } & \text { Treasurer } \\ \hline \text { Marina } & \text { Glenn } & \text { Ariel } \\ \text { Mima } & \text { Sung } & \text { Sherita } \\ \text { Nestor } & & \text { Westey } \\ \hline \end{array}$$

Ashley V.

### Problem 32

GAMES How many outcomes are possible for rolling three number cubes?

Ashley V.

### Problem 33

Find the probability of choosing a girl's name at random from 20 girls' names and 50 boys' names. Round to the nearest tenth percent. (Lesson 12 - 7)

Ashley V.

### Problem 34

Use the histogram. (Lesson $12-4$ )
How many years are there in each interval?

Ashley V.

### Problem 35

Use the histogram. (Lesson $12-4$ )
Which interval has the greatest number of animals?

Ashley V.

### Problem 36

Use the histogram. (Lesson $12-4$ )
How many of the animals in the histogram have a life span of more than 20 years?

Ashley V.

### Problem 37

Solve each inequality. Then graph the solution on a number line.
$$2 a-3 \geq 9$$

Ashley V.

### Problem 38

Solve each inequality. Then graph the solution on a number line.
$$4 c+4>32$$

Ashley V.

### Problem 39

Solve each inequality. Then graph the solution on a number line.
$$-2 y+3<9$$

Ashley V.

### Problem 40

Find each product. $$\frac{1}{6} \cdot \frac{1}{3}$$

Ashley V.

### Problem 41

Find each product. $$\frac{1}{6} \cdot \frac{1}{3}$$
$$\frac{2}{3} \cdot \frac{3}{6}$$

Ashley V.

### Problem 42

Find each product. $$\frac{1}{6} \cdot \frac{1}{3}$$
$$\frac{1}{3} \cdot \frac{1}{3} \cdot \frac{1}{3}$$

Ashley V.
Find each product. $$\frac{1}{6} \cdot \frac{1}{3}$$
$$\frac{3}{8} \cdot \frac{2}{7} \cdot \frac{1}{6}$$