Table of Contents
What Are Combinations?
A combination is a selection of items where order does not matter. Choosing {A,B,C} is the same as {C,B,A}. Combinations answer "how many ways can I choose k items from n?" and are fundamental to probability, statistics, and combinatorics.
The number of combinations is also called the binomial coefficient, written as C(n,k) or "n choose k". It appears in the binomial theorem, Pascal's triangle, and the binomial probability distribution.
Formula
Combinations vs Permutations
| Order Matters? | Formula | C(5,3) | |
|---|---|---|---|
| Combination | No | n!/(k!(n-k)!) | 10 |
| Permutation | Yes | n!/(n-k)! | 60 |
FAQ
When do I use combinations vs permutations?
Use combinations when order doesn't matter (choosing committee members, lottery numbers, card hands). Use permutations when order matters (rankings, passwords, race results).
What is Pascal's triangle?
Pascal's triangle arranges binomial coefficients in a triangular pattern where each number is the sum of the two above it. Row n gives C(n,0) through C(n,n).