A041 · Count without listing

Combinatorics laboratory

Choose a model, change the numbers and check small outcomes directly.

Before calculating, ask whether order matters and whether an object can occur more than once. The letters A, B, C… stand for distinct objects; AAB and ABA are different sequences.

Set up the problem

What would you like to count?

Objects or symbols (n) Positions or choices (k)

Multiplicities of identical letters (anagrams only)

Explained result

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Distinct cases

The lab lists cases only when there are few; the formula remains valid when a list would be too long. For anagrams, enter comma-separated multiplicities such as 2,2 for ANNA.