Video Lesson
📝 Practice Worksheets
🔑 Key Concepts
- A combination is used when order does not matter.
- The notation \( nCr \) means choosing \( r \) items from \( n \) total items.
- In a handshake problem, each handshake is a combination of 2 people.
- The formula is \( nCr = \frac{n!}{r!(n-r)!} \).
- The shortcut is to multiply the first \( r \) factors from \( n! \), then divide by \( r! \).
✏️ Worked Example
🧠 Math Vocabulary
- Combination: A selection of items where order does not matter.
- 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.
- Factorial: The product of a whole number and all positive whole numbers below it, such as \( 5! = 5 \times 4 \times 3 \times 2 \times 1 \).
- Order Does Not Matter: The same items count as one group even if they are listed in a different order.
- Handshake Problem: A classic combination problem where each pair of people creates one unique handshake.
💡 Main Idea
Combinations are used to count groups when order does not matter. The nCr formula and shortcut both help count how many unique groups can be made from a larger set.
📚 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 with permutations, where order does matter, and use counting strategies to solve probability problems.
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