1. What Are Combinations?

Combinations represent the number of ways to choose k items from a set of n items without regard to order. The formula for combinations is nCr = n! / (k!(n-k)!), where ! denotes factorial.

2. How To Calculate On TI-84 Plus

On a TI-84 Plus calculator, you can calculate combinations using the nCr function:

Steps to calculate on TI-84 Plus:

• Press the MATH button
• Navigate to the PRB (probability) menu
• Select option 3: nCr
• Enter the values: n nCr k
• Press ENTER to get the result

3. Importance Of Combinations

Details: Combinations are fundamental in probability, statistics, and combinatorics. They help calculate probabilities, analyze possible outcomes, and solve various mathematical problems involving selection without order.

4. Using The Calculator

Tips: Enter the total number of items (n) and the number of items to choose (k). Both values must be non-negative integers, and k must be less than or equal to n.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between combinations and permutations?
A: Combinations consider selection without order (nCr), while permutations consider selection with order (nPr).

Q2: What is the maximum value I can calculate?
A: The TI-84 Plus can handle values up to n=69 for accurate factorial calculations due to numerical limitations.

Q3: Can I calculate combinations for decimal numbers?
A: No, combinations are only defined for non-negative integers where k ≤ n.

Q4: What does "Error: Domain" mean on my TI-84?
A: This error occurs when k > n or when either value is negative, which are mathematically undefined.

Q5: Are there real-world applications of combinations?
A: Yes, combinations are used in lottery probability calculations, team selection, research sampling, and many other practical scenarios.