1. What is Combinations Calculation?

Combinations calculation determines the number of ways to choose items from a collection where order doesn't matter. It's fundamental in probability, statistics, and combinatorics.

2. How Does the Calculator Work?

The calculator uses the combinations formula:

Where:

• \( n \) — Total number of items
• \( r \) — Number of items to select
• \( ! \) — Factorial (product of all positive integers ≤ the number)

Explanation: The formula counts all possible subsets of size r from n items without considering order.

3. Importance of Combinations

Details: Combinations are essential in probability calculations, statistical sampling, cryptography, and any scenario where you need to count possible groupings.

4. Using the Calculator

Tips: Enter items as comma-separated values and the combination size (r). The calculator will show the total number of combinations and list them all.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between combinations and permutations?
A: Combinations don't consider order (AB = BA), while permutations do (AB ≠ BA).

Q2: What's the maximum number of items this can handle?
A: Practical limits depend on your browser/system memory when listing all combinations.

Q3: Can I use this for lottery probability calculations?
A: Yes, combinations are used to calculate lottery odds (e.g., 6 numbers from 49).

Q4: How are duplicate items handled?
A: The calculator automatically removes duplicate items from the input list.

Q5: What if r > number of items?
A: The calculator will show 0 combinations as it's impossible to choose more items than available.