Binomial Coefficient Calculator
Calculate combinations (nCr).
Formula first
Overview
The binomial coefficient represents the number of ways to choose a subset of r elements from a larger set of n distinct elements where the order of selection does not matter. It is a central component of the binomial theorem and Pascal's triangle, providing the coefficients for expanded algebraic expressions.
Symbols
Variables
tag = Total items n, tag = Items chosen r, calculate = Combinations
Apply it well
When To Use
When to use: Apply this formula when you are selecting items from a group and the sequence of selection is irrelevant. It assumes that items are distinct and cannot be chosen more than once in a single set.
Why it matters: This equation is essential in probability theory for determining the likelihood of specific outcomes in a series of independent events. It also appears in fields ranging from genetics to computer science algorithms and network topology.
Avoid these traps
Common Mistakes
- Confusing with Permutation (nPr).
- Calculation factorial overflow.
One free problem
Practice Problem
A committee of 3 members needs to be formed from a group of 10 employees. How many different unique committees can be created?
Solve for:
Hint: Apply the formula 10! / (3! × (10 - 3)!) and simplify the factorials.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Wikipedia: Binomial coefficient
- Discrete Mathematics and Its Applications by Kenneth H. Rosen
- Wikipedia: Dimensionless quantity
- IUPAC Gold Book: Dimensionless quantity
- Discrete Mathematics and Its Applications by Kenneth H. Rosen, 7th Edition (2012)
- Rosen, Kenneth H. Discrete Mathematics and Its Applications. 8th ed., McGraw-Hill Education, 2019.
- Wikipedia article 'Binomial coefficient'
- Britannica article 'Combinations and permutations'