Permutations and combinations calculator

Frequently asked questions

When should I use permutations versus combinations?

Use permutations when the order of selection matters — such as assigning first, second, and third place in a race. Use combinations when only the membership of the group matters and the order does not — such as choosing three people for a committee.

What do n and r represent?

n is the total number of items in the set you are choosing from, and r is the number of items you are selecting. Both must be non-negative whole numbers, and r cannot exceed n.

Why is nCr always smaller than or equal to nPr?

nCr divides nPr by r!, which collapses all the different orderings of the same selected group into a single count. Since r! is always at least 1, nCr can never exceed nPr, and the two are equal only when r is 0 or 1.

What happens when r equals n?

When every item in the set is selected, nPr equals n! (all arrangements of the full set) and nCr equals 1 (there is only one way to choose all items as an unordered group).