When do I use permutation vs combination?

Use a permutation when the order or arrangement matters (like ranking or seating); use a combination when only the selection matters and order is irrelevant (like choosing a team).

Is nPr always greater than nCr?

For r ≥ 2, ⁿPᵣ is greater than ⁿCᵣ because ⁿPᵣ = ⁿCᵣ × r!, and r! counts the different orderings that combinations ignore.

📐 Mathematics · JEE

Difference Between Permutation and Combination

Permutations and combinations are both ways of counting, but they differ in whether the order of selection matters.

In short

A permutation is an arrangement where order matters (nPr); a combination is a selection where order does not matter (nCr).

Permutation vs Combination — Comparison Table

Basis	Permutation	Combination
Order	Matters	Does not matter
Represents	Arrangement	Selection
Formula	ⁿPᵣ = n!/(n−r)!	ⁿCᵣ = n!/[r!(n−r)!]
Relation	ⁿPᵣ = ⁿCᵣ × r!	ⁿCᵣ = ⁿPᵣ / r!
Example	Arranging letters, ranks	Choosing a team, committee

Want to understand this fully? Read the Mathematics notes on this chapter.

Frequently Asked Questions — Permutation vs Combination

When do I use permutation vs combination?: Use a permutation when the order or arrangement matters (like ranking or seating); use a combination when only the selection matters and order is irrelevant (like choosing a team).
Is nPr always greater than nCr?: For r ≥ 2, ⁿPᵣ is greater than ⁿCᵣ because ⁿPᵣ = ⁿCᵣ × r!, and r! counts the different orderings that combinations ignore.