1. What is Permutation Without Repetition?

Permutation without repetition refers to the number of possible arrangements where order matters and items are not replaced after selection. In Python, this is calculated using math.perm(n, r) which gives the number of ways to choose r items from n items without repetition and with order.

2. How Does the Calculator Work?

The calculator uses the permutation formula:

Where:

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

Python Equivalent: This matches the behavior of Python's math.perm(n, r) function introduced in Python 3.8.

3. Importance of Permutation Calculation

Details: Permutations are fundamental in probability, statistics, and combinatorics. They're used in password generation, tournament scheduling, and any scenario where order matters.

4. Using the Calculator

Tips: Enter positive integers where n ≥ r ≥ 0. The calculator will compute the number of possible ordered arrangements.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between permutation and combination?
A: Permutation considers order (ABC ≠ BAC), while combination doesn't (ABC = BAC). Permutation counts more possibilities.

Q2: What if r > n?
A: The result is 0 since you can't select more items than available without replacement.

Q3: How does this differ from math.comb()?
A: math.comb() calculates combinations where order doesn't matter, while math.perm() calculates permutations where order matters.

Q4: What are some real-world applications?
A: Calculating possible race finish orders, password combinations, or seating arrangements.

Q5: How does this relate to factorial?
A: Permutation is related to factorial - when r = n, P(n,n) = n! (all items arranged).