1. What is Permutation Without Replacement?

Permutation without replacement refers to the number of possible arrangements when selecting r items from a set of n distinct items where order matters and items are not returned to the set after selection.

2. How Does the Calculator Work?

The calculator uses the permutation formula:

Where:

• \( n \) — Total number of distinct items
• \( r \) — Number of items to select and arrange
• \( ! \) — Factorial function (product of all positive integers up to that number)

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

3. Importance of Permutation Calculation

Details: Permutations are fundamental in probability, statistics, and combinatorics. They're used in password combinations, tournament scheduling, and many real-world arrangement problems.

4. Using the Calculator

Tips: Enter positive integers where n ≥ r. The calculator handles values up to n=170 (larger values exceed floating-point precision).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between permutation and combination?
A: Permutations consider order (ABC ≠ BAC), while combinations don't (ABC = BAC). Permutations give larger counts.

Q2: What if n = r?
A: When n = r, you're arranging all items, so P = n! (all possible orderings of the entire set).

Q3: What happens if r > n?
A: The result is 0 since you can't select more items than available without replacement.

Q4: How does this differ from permutation with replacement?
A: With replacement, the count is n^r (each selection is independent). Without replacement, the pool shrinks.

Q5: What are some real-world applications?
A: Calculating possible race finishing orders, unique password combinations, or seating arrangements.