1. What is Permutation With Repetition?

Permutation with repetition is an arrangement of objects where each object can be selected more than once. The order of selection matters, and items can be repeated in different positions.

2. How Does the Calculator Work?

The calculator uses the permutation with repetition formula:

Where:

• \( n \) — Number of distinct items to choose from
• \( r \) — Number of positions to fill

Explanation: For each of the r positions, there are n possible choices, leading to n multiplied by itself r times.

3. Importance of Permutation Calculation

Details: Permutations with repetition are fundamental in probability, statistics, and combinatorics. They're used in password combinations, license plate arrangements, and many real-world scenarios where order matters and items can repeat.

4. Using the Calculator

Tips: Enter positive integers for both n and r. The calculator will compute the total number of possible ordered arrangements where items can be repeated.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between permutation with and without repetition?
A: With repetition allows the same item to appear multiple times in the arrangement, while without repetition each item can only appear once.

Q2: What are some real-world examples?
A: Passwords (where digits/letters can repeat), combination locks, license plates, and DNA sequences are common examples.

Q3: How does this differ from combinations?
A: Permutations consider order important (ABC ≠ CBA), while combinations don't (ABC = CBA). Both can be with or without repetition.

Q4: What's the maximum value this calculator can handle?
A: It depends on your system's integer limits, but very large numbers may be displayed in scientific notation.

Q5: Can I use decimal numbers for n or r?
A: No, both n and r must be positive integers as you can't have a fraction of an item or position.