1. What Are Combinations?

Combinations represent the number of ways to choose r items from a set of n items without regard to order. This is different from permutations where order matters.

2. How To Calculate On TI-30X IIS

The TI-30X IIS calculator has a dedicated nCr function for calculating combinations:

Where:

• \( n \) — Total number of items
• \( r \) — Number of items to choose
• \( ! \) — Factorial (product of all positive integers up to that number)

3. Step-by-Step Instructions

Calculator Steps:

1. Enter the total number (n)
2. Press the [PRB] key (probability)
3. Select nCr (usually option 3)
4. Enter the number to choose (r)
5. Press [ENTER] to get the result

4. Practical Examples

Example 1: Choosing 3 students from 10 for a committee: 10 nCr 3 = 120 ways
Example 2: Selecting 5 cards from a 52-card deck: 52 nCr 5 = 2,598,960 possible hands
Example 3: Picking 2 toppings from 8 available: 8 nCr 2 = 28 combinations

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between nCr and nPr?
A: nCr is for combinations (order doesn't matter), nPr is for permutations (order matters).

Q2: Can I calculate nCr for large numbers?
A: The TI-30X IIS can handle n up to 69 for accurate nCr calculations due to factorial limitations.

Q3: What if r > n?
A: The calculator will return 0 since you cannot choose more items than available.

Q4: How do I calculate combinations manually?
A: Use the formula nCr = n! / (r! × (n-r)!) by calculating each factorial separately.

Q5: Are there real-world applications of combinations?
A: Yes! Used in probability, statistics, lottery calculations, team selections, and combinatorial mathematics.