1. What Are Permutations and Combinations?

Permutations and combinations are fundamental concepts in combinatorics that deal with counting arrangements of items. Permutations (P) consider order important, while combinations (C) do not.

2. How the Calculator Works

The calculator uses these formulas:

Where:

• \( n! \) — Factorial of n (n × (n-1) × ... × 1)
• \( r! \) — Factorial of r
• \( (n-r)! \) — Factorial of (n minus r)

Explanation: Permutations count ordered arrangements, while combinations count unordered groups.

3. When to Use Each

Permutations: Use when order matters (e.g., race rankings, password combinations).
Combinations: Use when order doesn't matter (e.g., committee selections, lottery numbers).

4. Using the Calculator

Tips: Enter total items (n) and selected items (r). Ensure n ≥ r. Select calculation type (permutation or combination).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between P and C?
A: Permutations consider order important (AB ≠ BA), combinations don't (AB = BA).

Q2: What if n = r?
A: For permutations, P(n,n) = n!. For combinations, C(n,n) = 1.

Q3: What are some real-world applications?
A: Permutations for password strength, combinations for probability calculations.

Q4: What's the maximum n value?
A: The calculator handles up to n=170 (limited by PHP's float precision).

Q5: What about repetition?
A: This calculator assumes no repetition. Different formulas apply when items can repeat.