Testinar Grade 8 math

Counting Principle and Permutations

Learn to reason about and solve Grade 8 problems involving Counting Principle and Permutations.

CH06-07 Statistics, Data, and Probability

Name
Date
Score: ____ / 8

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

A student can wear a shirt, pants, and shoes. There are \(3\) shirt colors, \(2\) pant types, and \(4\) shoe styles. How many different outfits are possible?
1. \(3 + 2 + 4 = 9\)
2. \(3 \times 2 \times 4 = 24\)
3. \(3^2 \times 4 = 36\)
4. \(24 + 3 = 27\)
A probability experiment involves flipping a coin (heads or tails) and rolling a die (1 through 6). How many different outcomes are possible?
1. \(2 + 6 = 8\)
2. \(2 \times 6 = 12\)
3. \(6^2 = 36\)
4. \(2 + 6 \times 2 = 14\)
A game requires picking a card from a deck of 10 cards and then spinning a spinner with 4 sections. How many possible results are there?
1. \(10 + 4 = 14\)
2. \(10 \times 4 = 40\)
3. \(10 - 4 = 6\)
4. \(4^{10}\)
A tree diagram shows that a choice has 3 branches first, then each branch splits into 2 more branches. How many final outcomes are there?
1. \(3 + 2 = 5\)
2. \(3 \times 2 = 6\)
3. \(3^2 = 9\)
4. \(2^3 = 8\)
In a game, you spin a spinner with 3 colors (red, yellow, green) and flip a coin (heads, tails). The table shows all outcomes. How many outcomes are there?
1. \(3 + 2 = 5\)
2. \(3 \times 2 = 6\)
3. \(2^3 = 8\)
4. \(3^2 = 9\)
A store sells T-shirts in 4 colors and 3 sizes. The diagram shows one color choice and one size choice. How many different T-shirt options are there?
1. \(4 + 3 = 7\)
2. \(4 \times 3 = 12\)
3. \(3^4 = 81\)
4. \(4 - 3 = 1\)
A student chooses a morning task (4 options) and an afternoon task (3 options). A partial tree diagram is drawn. How many final outcome branches are there?
1. \(4 + 3 = 7\)
2. \(4 \times 3 = 12\)
3. \(4^3 = 64\)
4. \(3^4 = 81\)
A game involves picking a number (1, 2, or 3) and a letter (A or B). The table lists some outcomes. How many total outcomes should the complete table show?
1. \(3 + 2 = 5\)
2. \(3 \times 2 = 6\)
3. \(2^3 = 8\)
4. \(3^2 = 9\)

Teacher and parent reference

Answer key and explanations

B. \(3 \times 2 \times 4 = 24\)
Multiply the number of choices at each step: \(3 \times 2 \times 4 = 24\) different outfits.
B. \(2 \times 6 = 12\)
Coin flip (2 outcomes) combined with die roll (6 outcomes): \(2 \times 6 = 12\) total outcomes.
B. \(10 \times 4 = 40\)
Card pick (10 choices) times spinner section (4 choices): \(10 \times 4 = 40\) possible results.
B. \(3 \times 2 = 6\)
Each of the 3 initial branches splits into 2 outcomes: \(3 \times 2 = 6\) final outcomes.
B. \(3 \times 2 = 6\)
From the table, count all cells: \(3\) colors times \(2\) coin outcomes \(= 6\) total outcomes.
B. \(4 \times 3 = 12\)
Each of the 4 colors can pair with each of the 3 sizes: \(4 \times 3 = 12\) total options.
B. \(4 \times 3 = 12\)
Each of the 4 morning branches splits into 3 afternoon branches: \(4 \times 3 = 12\) final outcomes.
B. \(3 \times 2 = 6\)
Count the cells in the table: \(3\) numbers \(\times\) \(2\) letters \(= 6\) total outcomes, shown as rows and columns.