Combination Calculator Calculate Combinations. Show Work.

Calculators Unique groups, no repeats

Combination Calculator

Use this page when you are choosing a subset from a larger set and the order of the chosen items does not create a new result.

Result

0

Enter values to calculate.

What your result means

The explanation updates with the current inputs.

Calculation work

    Live visual

    Fruit preview

    Previewing a small sample keeps the page fast and readable.

    Calculators Unique groups, no repeats

    Count distinct groups when order does not matter and you cannot reuse the same item.

    Practice this formula See exact answer pages

    When to use this

    Use this formula when the question matches this rule set

    Committee selection, choosing toppings without duplicates, and any pick-r-from-n question where A-B-C is the same group as C-B-A.

    What this result means

    Interpret the output, not just the number

    Each group is counted once. Reordering the same chosen items does not increase the total.

    Formula: C(n, r) = n! / (r!(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 size of the full pool.

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

    How to use it: Count each available choice once. If one item cannot be reused, do not count it twice.

    Example: From 9 volunteers, enter 9.

    r - number to choose

    This is the size of each final group.

    What to enter: Enter how many items end up in the selection.

    How to use it: Use the group size from the question, not the number left over.

    Example: A 4-person committee means enter 4.

    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: No.

    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