📝 Practice Worksheets
🔑 Key Concepts
- A combination is a selection where order does not matter.
- The notation \( nCr \) means choosing \( r \) items from \( n \) total items.
- The combination formula is \( nCr = \frac{n!}{r!(n-r)!} \).
- A shortcut is to multiply only the first \( r \) factors of \( n! \), then divide by \( r! \).
- Combination problems often include words like choose, select, committee, group, toppings, or handshakes.
✏️ Worked Examples
🧠 Math Vocabulary
- Combination: A selection of items where order does not matter.
- Permutation: An arrangement of items where order does matter.
- Factorial: The product of a whole number and all positive whole numbers below it, such as \( 5! = 5 \times 4 \times 3 \times 2 \times 1 \).
- nCr: A notation used to show the number of combinations of \( r \) items chosen from \( n \) total items.
- n: The total number of items available.
- r: The number of items being chosen.
- Order Does Not Matter: The same items count as one group even if they are listed in a different order.
💡 Main Idea
Combinations are used when choosing groups and order does not matter. The shortcut for \( nCr \) works because many factors cancel from the full factorial formula, leaving only the first \( r \) factors from \( n! \) divided by \( r! \).
📚 What You Should Already Know
Students should know how to multiply whole numbers, simplify fractions, understand factorial notation, and recognize whether order matters in a counting situation.
🚀 What Comes Next
Next, students can compare combinations and permutations, solve counting problems where order matters, and use combinations in probability situations.
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