1. What Are Permutations Without Repetition?

Permutations without repetition refer to the number of possible arrangements of a subset of items where the order matters and each item can be selected only once. This is common in problems like arranging people in line or selecting winners in a competition.

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)

Explanation: The formula calculates how many different ways you can arrange r items out of n total items when order matters and items aren't repeated.

3. When to Use Permutations

Details: Use permutations when:

• The order of selection matters (e.g., race rankings)
• Items cannot be selected more than once
• You need to count distinct arrangements

4. Using the Calculator

Tips:

• Enter positive integers only
• r must be ≤ n
• For n > 170, results may be approximate due to floating-point limitations

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).

Q2: What if I want to allow repetition?
A: Use the formula n^r instead, where each selection is independent.

Q3: What's the maximum n value I can calculate?
A: The calculator handles up to n=170 accurately. Beyond that, factorial values exceed floating-point precision.

Q4: Can I calculate permutations of non-integer values?
A: No, permutations only make sense for whole items (integers).

Q5: How is this used in real life?
A: Applications include password combinations, tournament scheduling, and statistical sampling.