Combination Calculator

Switch between combination and permutation logic by choosing whether order matters and whether repeated items are allowed. The result and formula update immediately. Open the full calculator for visuals and work.

Number of items

Number to choose

Does order matter? Choose combination when order does not matter, or permutation when it does. Are repeated items allowed? Allow the same item to be chosen more than once when repetition is part of the problem.

Result

0

Enter values to calculate.

Formula

Combination without repetition

C(n, r) = n! / (r!(n-r)!)

Order does not matter. Repeated items are not allowed.

What your result means

The explanation updates with the current inputs.

Four connected sections

Calculate ‣ question ‣ quiz ‣ apply!

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Calculators

Interactive tools for combinations, permutations, factorials, and related formulas.

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Answers

Short pages answering exact questions with the same values shown in the linked calculator.

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Quizzes

Practice sets with instant scoring, corrective feedback, and links to the right formula.

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Problems

Worked scenarios that explain whether order or repetition matters and why.

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Popular calculators

Calculators with visuals and work

Combination Calculator Count distinct groups when order does not matter and you cannot reuse the same item. Combination With Repetition Calculator Count distinct groups when order does not matter but the same item can be chosen more than once. Permutation Calculator Count ordered arrangements when position matters and each item can be used once. Permutation With Repetition Calculator Count ordered outcomes when each position matters and items can repeat.

Next useful pages

Exact answers and worked problems

What is 10 choose 3? 10 choose 3 without repeats is 120. What is 8P4? 8 permute 4 without repeats is 1,680. How many combinations of 12 items taken 2 at a time are there? 12 choose 2 without repeats is 66. Choose 4 Fruits From 9 This is a plain combination problem because order does not matter and each fruit can be used once. Arrange 6 Books On a Shelf This is a factorial or full permutation problem because all 6 distinct books are arranged in a row.