Probability

Combinations

Formula

C(n, r) = n! / (r! × (n−r)!)

What is Combinations?

Combinations count the number of ways to choose r items from n items where order does not matter. The exclamation mark denotes factorial.

Variables

n
n — Total number of items
r
r — Number of items to choose
!
! — Factorial (e.g., 5! = 5×4×3×2×1)

Worked Examples

Example 1

How many ways can you choose 3 items from 7?

Solution:

C(7,3) = 7! / (3! × 4!) = 5040 / (6 × 24) = 5040 / 144 = 35

Frequently Asked Questions

Related Formulas

P(Event) = (Number of favorable outcomes) / (Total number of outcomes)

P(n, r) = n! / (n−r)!

Binomial Probability

P(X = k) = C(n, k) × pᵏ × (1−p)ⁿ⁻ᵏ

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