Module 2 · Probability Foundations · Topic 10

Permutations & Combinations

Permutation vs Combination. A permutation is an arrangement where order matters. A combination is a selection where order does not matter.

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Key formulas

Permutations

P(n, r) = n! / (n − r)!

Combinations

C(n, r) = n! / (r! × (n − r)!)

From the Probability Foundations formula sheet

Conditional Probability: P(A | B) = P(A and B) / P(B) — Probability of A after restricting attention to cases where B occurred.
Bayes' Theorem: P(A | B) = P(B | A)P(A) / P(B) — Updates a prior probability after observing evidence.

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Worked example

Worked Example

Choosing a president, VP, and secretary from 10 people (order matters): P(10, 3) = 10!/7! = 720. Choosing a 3-person committee from 10 (order doesn’t matter): C(10, 3) = 720/6 = 120.

When to use it

Quick Decision Rule

Ask: “Does the order of selection matter?” If yes, use permutations. If no, use combinations. Combinations are always smaller than or equal to permutations for the same n and r.

Related glossary terms

Independence: Two events are independent when one occurring does not change the probability of the other. Example: Two separate fair coin flips are independent.

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