1. What is Combination Without Repetition?

Combination without repetition calculates how many ways you can choose 3 items from a larger set where order doesn't matter and items aren't repeated. This is common in probability, statistics, and combinatorics.

2. How Does the Calculator Work?

The calculator uses the combination formula:

Where:

• \( n \) — Total number of items
• \( ! \) — Factorial function (product of all positive integers up to that number)
• \( C \) — Number of possible combinations

Explanation: The formula divides the total permutations by the number of ways to arrange the selected items (3!) and the unselected items ((n-3)!).

3. Importance of Combination Calculation

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

4. Using the Calculator

Tips: Enter the total number of items (must be ≥3). The calculator will compute how many unique groups of 3 can be formed.

5. Frequently Asked Questions (FAQ)

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

Q2: Why does n need to be ≥3?
A: You can't form groups of 3 from fewer than 3 items. The formula would give 0 or undefined results.

Q3: What are some real-world applications?
A: Lottery odds calculation, team formation possibilities, experimental design combinations, etc.

Q4: How does this scale with larger n values?
A: The number of combinations grows rapidly (n³/6 for large n). For n=10 → 120 combinations, n=20 → 1140.

Q5: Can this calculate combinations of other sizes?
A: This specific calculator only handles groups of 3. The general formula is C(n,k) = n!/(k!(n-k)!).