Permutations and Combinations (Copy)
11 Permutations and Combinations – Cheat Sheet
11.1 Difference Between Permutations and Combinations
- Permutations (order matters): Different arrangements of items.
Example: ABC and BAC are different permutations. - Combinations (order does NOT matter): Different selections of items.
Example: ABC and BAC are the same combination.
11.2 Factorial Notation
- n! = n × (n – 1) × (n – 2) × … × 3 × 2 × 1
- 0! = 1 (by definition)
11.3 Formulas
- Permutation:
P(n, r) = nPr = n! / (n – r)! - Combination:
C(n, r) = nCr = n! / [r!(n – r)!]
When to Use Each
- Permutation: Order matters (arranging books, assigning seats, ranking results).
- Combination: Order does not matter (choosing a team, selecting items).
Examples
- Permutation example:
How many ways to arrange 4 books out of 7?
n = 7, r = 4
7P4 = 7! / (7 – 4)! = (7 × 6 × 5 × 4) = 840 - Combination example:
How many ways to choose 4 students out of 7?
7C4 = 7! / (4! × 3!) = 35