Permutations (nPr)
Count how many ways r items can be arranged from n when order matters
Interactive Sandbox
Adjust values in real-time and observe mathematical cause-and-effect
Central Tendency & Dispersion: Measures the central average (mean) and spread of variability (standard deviation).
Variable Mechanics
Roles, constraints & impacts
Total Items (n)
Formula Parameter
Items Arranged (r)
Formula Parameter
At a Glance
Gotchas, units & real-world use
Formula Nature & Mechanics
Central Tendency & Dispersion: Measures the central average (mean) and spread of variability (standard deviation).
Common Mistakes & Traps
- Confusing Population Standard Deviation (divide by N) with Sample Standard Deviation (divide by n - 1 for Bessel correction).
- Assuming all distributions are normal (skewed distributions make the median more reliable than mean).
- Outliers disproportionately distort the mean and variance.
Dimensional Analysis & Units
Mean & SD share the same unit as original data; Variance is in [Unit]².
Real-World & Industry Application
Quality control tolerances in manufacturing, stock market volatility metrics, clinical medical trials, and academic grading curves.
Worked Example: Permutations (nPr)
Given:
- n = 5
- r = 2
- 5P2 = 5! / 3!
- = 120 / 6
- = 20
Answer: 20
Frequently Asked Questions
What is the Permutations (nPr) formula?
nPr = n! / (n - r)!. Count how many ways r items can be arranged from n when order matters.
How do I calculate Permutations (nPr)?
Enter Total Items (n) (n), Items Arranged (r) (r) into the calculator. It applies nPr = n! / (n - r)! and shows every step of the working.
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