Combination Calculator Calculate Combinations. Show Work.

Calculators Groups where reuse is allowed

Combination With Repetition Calculator

Use this page when you can choose the same option multiple times, but reordering the same set 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 Groups where reuse is allowed

    Count distinct groups when order does not matter but the same item can be chosen more than once.

    Practice this formula See exact answer pages

    When to use this

    Use this formula when the question matches this rule set

    Ice cream scoops, donut assortments, or fruit bowls where repeating one flavor or fruit is allowed.

    What this result means

    Interpret the output, not just the number

    Each multiset is counted once. Strawberry-vanilla-vanilla matches vanilla-strawberry-vanilla.

    Formula: C(n + r - 1, r) = (n + r - 1)! / (r!(n-1)!)

    Calculator inputs

    Know what to enter in each field

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

    n - available item types

    This is how many different options exist.

    What to enter: Enter the number of distinct item types, flavors, or categories you can choose from.

    How to use it: Count each type once, even when the same type can be chosen more than once.

    Example: With 5 flavors available, enter 5.

    r - selections to make

    This is how many picks go into the final group.

    What to enter: Enter the total number of selections.

    How to use it: Use the basket, scoop, or box size from the question.

    Example: A 3-scoop order 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: 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: Yes.

    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