1. What is Permutation (nPr)?

Permutation (nPr) represents the number of possible arrangements of 'r' items from a set of 'n' distinct items where order matters. It's a fundamental concept in combinatorics and probability.

2. How Does the Calculator Work?

The calculator uses the permutation formula:

Where:

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

Explanation: The numerator counts all possible arrangements of all items, while the denominator removes arrangements of items not selected.

3. Importance of Permutations

Details: Permutations are essential in probability, statistics, cryptography, and many real-world applications like password generation, tournament scheduling, and seating arrangements.

4. Using the Calculator

Tips: Enter positive integers where n ≥ r. The calculator will compute the number of possible ordered arrangements.

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). Use nCr for combinations.

Q2: What if n = r?
A: When n = r, nPr = n! (all items arranged in all possible orders).

Q3: What's the maximum value this calculator can handle?
A: Due to factorial growth, values above 170 may cause overflow. For n > 20, approximations may be needed.

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 is this different from arrangements with repetition?
A: This calculates arrangements without repetition. For arrangements with repetition, the count is simply n^r.