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How to Calculate Combinations

Calculate the number of ways to choose r items from n items.

The Formula

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

The combinations formula uses the mathematical relationship: C(n,r) = n! / r!(n-r)!. Each variable in the formula represents a measurable quantity that affects the final result.

Step-by-Step Method

  1. 1Identify all input values needed for the combinations calculation.
  2. 2Substitute your known values into the formula: C(n,r) = n! / r!(n-r)!.
  3. 3Perform the arithmetic operations in the correct order (PEMDAS/BODMAS).
  4. 4Check that your result has the correct units and is within a reasonable range.
  5. 5Verify using the interactive Combinations Calculator to confirm your answer.

Related Topics

combinationschoosecombinatorics

Use the Interactive Calculator

Skip the manual math — get instant results with our free Combinations calculator.

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