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Counting: Permutations & Combinations — Easy Worksheet 2
Grade 11 · Whoobee Name: ____________________ Date: __________
Find each number. Decide first whether order matters.
How to solve
Counting principle: multiply the number of choices at each step. n! = n × (n - 1) × ... × 1 counts ways to arrange n things. When order matters (1st, 2nd, 3rd), use P(n, r) = n! ÷ (n - r)!. When order does not matter (a group or committee), use C(n, r) = n! ÷ (r! × (n - r)!).
Example
You have 5 shirts, 3 pairs of pants and 3 pairs of shoes. How many different outfits can you make?
Answer: 45
Not quite. The answer is
💡 Each outfit is one shirt, one pair of pants and one pair of shoes, so by the counting principle multiply: 3 × 4 × 3 = 36 outfits.
✓ Correct!
Not quite. The answer is
💡 Each outfit is one shirt, one pair of pants and one pair of shoes, so by the counting principle multiply: 3 × 4 × 3 = 36 outfits.
💡 How to solve: Counting: Permutations & Combinations
Counting principle: multiply the number of choices at each step. n! = n × (n - 1) × ... × 1 counts ways to arrange n things. When order matters (1st, 2nd, 3rd), use P(n, r) = n! ÷ (n - r)!. When order does not matter (a group or committee), use C(n, r) = n! ÷ (r! × (n - r)!).
Try a similar one
You have 6 shirts, 4 pairs of pants and 3 pairs of shoes. How many different outfits can you make?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 4! means multiply every whole number from 4 down to 1: 4 × 3 × 2 × 1 = 24.
✓ Correct!
Not quite. The answer is
💡 4! means multiply every whole number from 4 down to 1: 4 × 3 × 2 × 1 = 24.
💡 How to solve: Counting: Permutations & Combinations
Counting principle: multiply the number of choices at each step. n! = n × (n - 1) × ... × 1 counts ways to arrange n things. When order matters (1st, 2nd, 3rd), use P(n, r) = n! ÷ (n - r)!. When order does not matter (a group or committee), use C(n, r) = n! ÷ (r! × (n - r)!).
Try a similar one
You have 4 shirts, 4 pairs of pants and 2 pairs of shoes. How many different outfits can you make?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Order matters and all 3 books are used. There are 3 choices for the first spot, 2 for the next, and so on, so the number of orders is 3! = 3 × 2 × 1 = 6.
✓ Correct!
Not quite. The answer is
💡 Order matters and all 3 books are used. There are 3 choices for the first spot, 2 for the next, and so on, so the number of orders is 3! = 3 × 2 × 1 = 6.
💡 How to solve: Counting: Permutations & Combinations
Counting principle: multiply the number of choices at each step. n! = n × (n - 1) × ... × 1 counts ways to arrange n things. When order matters (1st, 2nd, 3rd), use P(n, r) = n! ÷ (n - r)!. When order does not matter (a group or committee), use C(n, r) = n! ÷ (r! × (n - r)!).
Try a similar one
You have 4 shirts, 3 pairs of pants and 3 pairs of shoes. How many different outfits can you make?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Each outfit is one shirt, one pair of pants and one pair of shoes, so by the counting principle multiply: 3 × 4 × 2 = 24 outfits.
✓ Correct!
Not quite. The answer is
💡 Each outfit is one shirt, one pair of pants and one pair of shoes, so by the counting principle multiply: 3 × 4 × 2 = 24 outfits.
💡 How to solve: Counting: Permutations & Combinations
Counting principle: multiply the number of choices at each step. n! = n × (n - 1) × ... × 1 counts ways to arrange n things. When order matters (1st, 2nd, 3rd), use P(n, r) = n! ÷ (n - r)!. When order does not matter (a group or committee), use C(n, r) = n! ÷ (r! × (n - r)!).
Try a similar one
You have 5 shirts, 2 pairs of pants and 3 pairs of shoes. How many different outfits can you make?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 3! means multiply every whole number from 3 down to 1: 3 × 2 × 1 = 6.
✓ Correct!
Not quite. The answer is
💡 3! means multiply every whole number from 3 down to 1: 3 × 2 × 1 = 6.
💡 How to solve: Counting: Permutations & Combinations
Counting principle: multiply the number of choices at each step. n! = n × (n - 1) × ... × 1 counts ways to arrange n things. When order matters (1st, 2nd, 3rd), use P(n, r) = n! ÷ (n - r)!. When order does not matter (a group or committee), use C(n, r) = n! ÷ (r! × (n - r)!).
Try a similar one
You have 2 shirts, 2 pairs of pants and 3 pairs of shoes. How many different outfits can you make?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Order matters and all 7 books are used. There are 7 choices for the first spot, 6 for the next, and so on, so the number of orders is 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040.
✓ Correct!
Not quite. The answer is
💡 Order matters and all 7 books are used. There are 7 choices for the first spot, 6 for the next, and so on, so the number of orders is 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040.
💡 How to solve: Counting: Permutations & Combinations
Counting principle: multiply the number of choices at each step. n! = n × (n - 1) × ... × 1 counts ways to arrange n things. When order matters (1st, 2nd, 3rd), use P(n, r) = n! ÷ (n - r)!. When order does not matter (a group or committee), use C(n, r) = n! ÷ (r! × (n - r)!).
Try a similar one
You have 2 shirts, 2 pairs of pants and 3 pairs of shoes. How many different outfits can you make?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Each outfit is one shirt, one pair of pants and one pair of shoes, so by the counting principle multiply: 5 × 2 × 3 = 30 outfits.
✓ Correct!
Not quite. The answer is
💡 Each outfit is one shirt, one pair of pants and one pair of shoes, so by the counting principle multiply: 5 × 2 × 3 = 30 outfits.
💡 How to solve: Counting: Permutations & Combinations
Counting principle: multiply the number of choices at each step. n! = n × (n - 1) × ... × 1 counts ways to arrange n things. When order matters (1st, 2nd, 3rd), use P(n, r) = n! ÷ (n - r)!. When order does not matter (a group or committee), use C(n, r) = n! ÷ (r! × (n - r)!).
Try a similar one
Evaluate 5!
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 6! means multiply every whole number from 6 down to 1: 6 × 5 × 4 × 3 × 2 × 1 = 720.
✓ Correct!
Not quite. The answer is
💡 6! means multiply every whole number from 6 down to 1: 6 × 5 × 4 × 3 × 2 × 1 = 720.
💡 How to solve: Counting: Permutations & Combinations
Counting principle: multiply the number of choices at each step. n! = n × (n - 1) × ... × 1 counts ways to arrange n things. When order matters (1st, 2nd, 3rd), use P(n, r) = n! ÷ (n - r)!. When order does not matter (a group or committee), use C(n, r) = n! ÷ (r! × (n - r)!).
Try a similar one
You have 6 shirts, 2 pairs of pants and 3 pairs of shoes. How many different outfits can you make?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Order matters and all 4 books are used. There are 4 choices for the first spot, 3 for the next, and so on, so the number of orders is 4! = 4 × 3 × 2 × 1 = 24.
✓ Correct!
Not quite. The answer is
💡 Order matters and all 4 books are used. There are 4 choices for the first spot, 3 for the next, and so on, so the number of orders is 4! = 4 × 3 × 2 × 1 = 24.
💡 How to solve: Counting: Permutations & Combinations
Counting principle: multiply the number of choices at each step. n! = n × (n - 1) × ... × 1 counts ways to arrange n things. When order matters (1st, 2nd, 3rd), use P(n, r) = n! ÷ (n - r)!. When order does not matter (a group or committee), use C(n, r) = n! ÷ (r! × (n - r)!).
Try a similar one
You have 4 shirts, 5 pairs of pants and 2 pairs of shoes. How many different outfits can you make?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Each outfit is one shirt, one pair of pants and one pair of shoes, so by the counting principle multiply: 4 × 3 × 3 = 36 outfits.
✓ Correct!
Not quite. The answer is
💡 Each outfit is one shirt, one pair of pants and one pair of shoes, so by the counting principle multiply: 4 × 3 × 3 = 36 outfits.
💡 How to solve: Counting: Permutations & Combinations
Counting principle: multiply the number of choices at each step. n! = n × (n - 1) × ... × 1 counts ways to arrange n things. When order matters (1st, 2nd, 3rd), use P(n, r) = n! ÷ (n - r)!. When order does not matter (a group or committee), use C(n, r) = n! ÷ (r! × (n - r)!).
Try a similar one
You have 4 shirts, 2 pairs of pants and 3 pairs of shoes. How many different outfits can you make?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Counting: Permutations & Combinations — Easy Worksheet 2
Find each number. Decide first whether order matters.