1. What is Permutation?

Permutation refers to the arrangement of objects in a specific order. The number of permutations of n objects taken r at a time is calculated using the formula P(n,r) = n!/(n-r)!.

2. How Does the Calculator Work?

The calculator uses the permutation formula:

Where:

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

Explanation: The formula calculates the number of possible arrangements when order matters.

3. Importance of Permutation Calculation

Details: Permutations are essential in probability, statistics, and combinatorics. They're used in password combinations, seating arrangements, and tournament scheduling.

4. Using the Calculator

Tips: Enter positive integers where n ≥ r. 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: Permutations consider order (ABC ≠ BAC), while combinations don't (ABC = BAC).

Q2: How is this different on a TI-84 calculator?
A: On TI-84, use MATH → PRB → nPr or the formula directly: n!/(n-r)!

Q3: What if n = r?
A: P(n,n) = n! (all items arranged in all possible orders).

Q4: What's the maximum n value this can handle?
A: Due to factorial growth, n > 170 will overflow standard floating-point representation.

Q5: Can I use this for non-integer values?
A: The standard permutation formula requires integer n and r with n ≥ r ≥ 0.