Combination Calculator Calculate Combinations. Show Work.

Calculators Ordered selections, no repeats

Permutation Calculator

Use this page when swapping two selected items produces a different outcome and repeated use is not allowed.

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What your result means

The explanation updates with the current inputs.

Calculation work

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    Previewing a small sample keeps the page fast and readable.

    Calculators Ordered selections, no repeats

    Count ordered arrangements when position matters and each item can be used once.

    Practice this formula See exact answer pages

    When to use this

    Use this formula when the question matches this rule set

    Officer roles, race podiums, seating in a row, or arranging books on a shelf.

    What this result means

    Interpret the output, not just the number

    Each ordering is a new result. ABC and BAC count separately.

    Formula: P(n, r) = n! / (n-r)!

    Calculator inputs

    Know what to enter in each field

    Match the wording in the question to these fields before you interpret the result.

    n - items to choose from

    This is the full set of distinct candidates.

    What to enter: Enter the total number of distinct items available.

    How to use it: Use this when each item can appear at most once and position matters.

    Example: From 10 candidates for officer roles, enter 10.

    r - ordered positions

    This is how many ordered slots you fill.

    What to enter: Enter the number of positions or places in the arrangement.

    How to use it: If first, second, and third all matter, r is 3.

    Example: A podium with gold, silver, and bronze means enter 3.

    Does order matter on this page?

    This page keeps the order rule fixed in the background so the calculator stays in the same formula family.

    How this page works: Yes.

    How to use it: Use the combination pages when only the final group matters. Use the permutation pages when changing the order creates a different result.

    Example: A podium uses yes, but a committee uses no.

    Are repeated items allowed?

    This is the one mode control on the dedicated page. It switches between the repeat and no-repeat version of the same formula family.

    How this page opens: No.

    How to use it: Choose yes when reuse is allowed. Choose no when each available item can be used at most once.

    Example: Three scoops from five flavors uses yes, but four different fruits uses no.

    Worked examples

    Quick checks with realistic inputs