1. What is the Permutations Formula?

The permutations formula calculates the number of possible arrangements of a set of items where order matters. The formula is simply the factorial of the number of items.

2. How Does the Calculator Work?

The calculator uses the permutations formula:

Where:

• \( n \) — Number of distinct items
• \( ! \) — Factorial operator (product of all positive integers ≤ n)

Explanation: For n items, there are n! (n factorial) possible ordered arrangements.

3. Importance of Permutations Calculation

Details: Permutations are fundamental in probability, statistics, and combinatorics. They're used to calculate possible outcomes in ordered arrangements.

4. Using the Calculator

Tips: Enter the number of items (n). The calculator supports values from 0 to 170 (170! ≈ 7.26e+306).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between permutations and combinations?
A: Permutations consider order (ABC ≠ BAC), while combinations don't (ABC = BAC).

Q2: What is 0! ?
A: By definition, 0! = 1 (there's exactly one way to arrange zero items).

Q3: Why is there a limit of 170?
A: Beyond 170!, numbers exceed PHP's floating point maximum value.

Q4: How are permutations used in real life?
A: Used in cryptography, game theory, scheduling problems, and anywhere order matters.

Q5: What if items aren't distinct?
A: For repeated items, divide by the factorials of identical items' counts.