1. What Are Permutations?

Permutations refer to the number of ways to arrange 'r' items from a set of 'n' distinct items where order matters. Unlike combinations, the sequence of selection is important in permutations.

2. How Does the Calculator Work?

The calculator uses the permutations formula:

Where:

• \( n \) — Total number of items
• \( r \) — Number of items selected
• \( ! \) — Factorial function (product of all positive integers ≤ the number)

Explanation: The formula calculates the number of possible ordered arrangements when selecting 'r' items from 'n' items without replacement.

3. When to Use Permutations

Details: Use permutations when the order/arrangement matters, such as in passwords, race results, or seating arrangements. If order doesn't matter, use combinations instead.

4. Using the Calculator

Tips: Enter positive integers where n ≥ r. The calculator automatically handles the factorial calculations and provides the number of possible permutations.

5. Frequently Asked Questions (FAQ)

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

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 may return infinity due to PHP's number size limits.

Q4: Can I use this for non-integer values?
A: No, permutations are only defined for non-negative integers where n ≥ r ≥ 0.

Q5: How are permutations used in real life?
A: They're used in probability, cryptography, game design, and anywhere order-sensitive arrangements are needed.