Combinations & Permutations

📖 Combinations vs Permutations

Combinations — order does NOT matter

C(n,r) = n! / (r!(n−r)!)

Choosing 3 pizza toppings from 10

Permutations — order DOES matter

P(n,r) = n! / (n−r)!

Arranging 3 runners on a podium from 10

n

Total itemsThe total number of items to choose from

r

Items chosenHow many items you are selecting

!

Factorialn! = n × (n-1) × (n-2) × ... × 1 e.g. 5! = 120

C

How many ways to choose 3 from 5? (order doesn't matter)C(5,3) = 5! / (3! × 2!) = 120 / (6×2) = 10

P

How many ways to arrange 3 from 5? (order matters)P(5,3) = 5! / 2! = 120 / 2 = 60

n (total)

r (chosen)

Result will appear here