1. What is Permutation?

Permutation refers to the arrangement of objects in a specific order. It calculates the number of ways to arrange r items from a set of n distinct items where order matters.

2. How Does the Calculator Work?

The calculator uses the permutation formula:

Where:

• \( n \) — Total number of items
• \( r \) — Number of items selected
• \( n! \) — Factorial of n (n × (n-1) × ... × 1)
• \( (n - r)! \) — Factorial of (n - r)

Explanation: The formula calculates the number of possible arrangements when selecting r items from n items where order matters.

3. Importance of Permutation Calculation

Details: Permutation calculations are essential in probability theory, statistics, combinatorics, and various real-world applications like password generation, tournament scheduling, and experimental design.

4. Using the Calculator

Tips: Enter the total number of items (n) and the number of items to select (r). Both values must be non-negative integers, and r cannot exceed n.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between permutation and combination?
A: Permutation considers order of selection (ABC ≠ CBA), while combination does not (ABC = CBA). Use permutation when order matters.

Q2: What if r = 0?
A: When r = 0, there is exactly 1 way to arrange zero items (the empty arrangement).

Q3: What are some real-world applications of permutations?
A: Password combinations, race finishing orders, committee assignments with specific roles, and seating arrangements.

Q4: Why does n need to be greater than or equal to r?
A: You cannot select more items than available. The formula requires that r ≤ n for valid calculation.

Q5: How does permutation relate to factorial?
A: When r = n, permutation equals n! (all items arranged in all possible orders).