1. What is Combination?

A combination is a selection of items from a larger set where the order of selection does not matter. It's a fundamental concept in combinatorics and probability.

2. How Does the Calculator Work?

The calculator uses the combination formula:

Where:

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

Explanation: The formula calculates how many ways you can choose r items from n items without considering the order.

3. Importance of Combinations

Details: Combinations are essential in probability calculations, statistical analysis, and various real-world applications like lottery odds, team selections, and password combinations.

4. Using the Calculator

Tips: Enter the total number of items (n) and the number to choose (r). Both must be positive integers with n ≥ r.

5. Frequently Asked Questions (FAQ)

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

Q2: What if r > n?
A: The result is 0 since you can't choose more items than available.

Q3: What's the largest n this calculator can handle?
A: Due to factorial growth, n > 170 will cause overflow. For large n, use logarithmic approaches.

Q4: How is this used in real life?
A: Used in lottery odds, team selections, password combinations, and statistical sampling.

Q5: What about combinations with repetition?
A: This calculator handles combinations without repetition. The formula changes to C(n+r-1, r) when repetition is allowed.