1. What is Permutation?

Permutation refers to the arrangement of objects in a specific order. In word permutations, it calculates how many different ways you can arrange letters from a given set.

2. How Does the Calculator Work?

The calculator uses the permutation formula:

Where:

• \( n \) — Total number of items
• \( r \) — Number of items selected for arrangement
• \( ! \) — Factorial (product of all positive integers up to that number)

Explanation: The formula calculates the number of possible ordered arrangements when selecting r items from a set of n distinct items.

3. Importance of Permutation Calculation

Details: Permutation calculations are essential in probability, statistics, cryptography, and various fields where order matters in arrangements.

4. Using the Calculator

Tips: Enter the total number of items (n) and the number to be selected (r). Both must be positive integers with n ≥ r.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between permutation and combination?
A: Permutation considers order (ABC is different from BAC), while combination doesn't (ABC and BAC are the same).

Q2: What if n = r?
A: When n = r, you're calculating all possible arrangements of all items, which is simply n!.

Q3: What's the maximum value this calculator can handle?
A: Due to factorial growth, values above 170 will return infinity due to PHP's float limitations.

Q4: Can this be used for word arrangements?
A: Yes, if all letters are distinct. For repeated letters, you need to divide by the factorial of repeated counts.

Q5: What are some practical applications?
A: Password combinations, tournament scheduling, cryptography, and any scenario where order matters.