📝 Practice Worksheets
🔑 Key Concepts
- A permutation is an arrangement where order matters.
- The notation \( nPr \) means arranging \( r \) items from \( n \) total items.
- The formula is \( nPr=\frac{n!}{(n-r)!} \).
- The shortcut is to multiply the first \( r \) factors of \( n! \).
💡 Main Idea
Permutations are used when arranging items and the order matters. For example, choosing the first, second, and third hitters in a lineup is different from choosing the same players in a different order.
✏️ Worked Example
🧠 Math Vocabulary
- Permutation: An arrangement of items where order matters.
- Arrangement: A specific order or placement of items.
- nPr: A notation for arranging \( r \) items from \( n \) total items.
- Factorial: The product of a number and all positive whole numbers below it, such as \( 5! = 5 \times 4 \times 3 \times 2 \times 1 \).
- n: The total number of items available.
- r: The number of items being arranged.
- Order Matters: Changing the order creates a different outcome.
📚 What You Should Already Know
Students should know how to multiply whole numbers, understand factorial notation, and recognize whether a counting situation depends on order.
🚀 What Comes Next
Next, students can compare permutations with combinations, where order does not matter, and use both strategies in probability and counting problems.
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