Combinations (nCr)
Count how many ways r items can be chosen from n when order does not matter
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 Chosen (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: Combinations (nCr)
Given:
- n = 5
- r = 2
- 5C2 = 5! / (2! × 3!)
- = 120 / (2 × 6)
- = 120 / 12
- = 10
Answer: 10
Frequently Asked Questions
What is the Combinations (nCr) formula?
nCr = n! / (r! × (n - r)!). Count how many ways r items can be chosen from n when order does not matter.
How do I calculate Combinations (nCr)?
Enter Total Items (n) (n), Items Chosen (r) (r) into the calculator. It applies nCr = n! / (r! × (n - r)!) and shows every step of the working.
Related Statistics Calculators
Partner Spotlight
