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
• \( r \) — 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 regard to order.

3. Importance of Combination Calculation

Details: Combinations are used in probability, statistics, and many real-world applications like lottery odds, team selection, and experiment design.

4. Using the Calculator

Tips: Enter positive integers where n ≥ r ≥ 0. The calculator will compute the number of possible combinations.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between combination and permutation?
A: Combinations consider selection order irrelevant (AB = BA), while permutations treat them as different.

Q2: What if r > n?
A: By definition, C(n, r) = 0 when r > n since you can't choose more items than you have.

Q3: What is 0! (zero factorial)?
A: 0! is defined as 1, which makes the formula work when r = 0 or r = n.

Q4: How does this relate to Pascal's Triangle?
A: Each entry in Pascal's Triangle corresponds to C(n, r) for row n and position r.

Q5: What are some practical applications?
A: Used in probability calculations, lottery odds, statistical sampling, and combinatorial design.