1. What Is The Combination Formula?

The combination formula calculates the number of ways to choose r items from a set of n items without regard to order. It's a fundamental concept in combinatorics and probability theory.

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 function (product of all positive integers up to that number)

Explanation: The formula divides the total permutations by the number of ways to arrange the selected items, eliminating order considerations.

3. Importance Of Combination Calculation

Details: Combinations are essential in probability, statistics, gambling, computer science, and many real-world applications where selection order doesn't matter.

4. Using The Calculator

Tips: Enter the total number of items (n) and the number to choose (r). Both values must be non-negative integers, and r cannot exceed n.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between combinations and permutations?
A: Combinations consider selection only (order doesn't matter), while permutations consider both selection and arrangement (order matters).

Q2: What if r = 0 or r = n?
A: C(n, 0) = 1 (one way to choose nothing) and C(n, n) = 1 (one way to choose everything).

Q3: Are there limitations to this formula?
A: The formula assumes all items are distinct. For items with duplicates, different formulas apply.

Q4: What is the maximum value this calculator can handle?
A: Due to factorial computation limitations, values above 170 may cause overflow issues in standard implementations.

Q5: Can combinations be calculated for non-integer values?
A: The standard combination formula is defined only for non-negative integers where r ≤ n.