Math Tools

Permutations & Combinations

Calculate arrangements and selections with ease

nPr

Permutations

n! / (n-r)!
Result
—
nCr

Combinations

n! / (r!(n-r)!)
Result
—

Quick Quiz: P or C?

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Does the order matter?

When to Use Each

Permutations (Order Matters)

Use when the arrangement order is important. Example: How many ways can 3 people finish a race from 10 runners?

P(10,3) = 720 ways
Combinations (Order Doesn't Matter)

Use when you're just selecting items without regard to order. Example: How many ways can you choose 3 people for a committee from 10?

C(10,3) = 120 ways
Quick Memory Trick

Permutation = Position matters (like race Places)
Combination = Just Choosing (like a Committee)

Relationship

Permutations are always ≥ combinations because order creates more possibilities.

P(n,r) = C(n,r) × r!