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Ordered Sequences with Replacement: Count & List

Count ordered length-r sequences from n reusable types and enumerate supported small examples.

Calculator inputs

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Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Three choices for each of two positions give nine ordered sequences.

Number of sequences = n^r

Enter these known values and leave the other values blank.

Inputs are integers. The retained upper bound is 100,000 for each input. A selection of zero objects has one outcome: the empty selection.
Distinct types are labeled A, B, C and so on in examples. Replacement permits repeated use of a type; ordering treats different position sequences as different outcomes.
Arithmetic uses 64 significant decimal digits. Large counts can be rounded, and scientific notation is approximate; this tool does not certify every digit of an arbitrarily large integer.
Counts are available beyond the small-example listing ranges. A list appears only where the complete enumeration fits the supported range.
At least one available type is required in replacement/combined modes. Without-replacement selections with r > n have zero outcomes in combined comparisons.

Yes. Order makes AB and BA different; replacement allows outcomes such as AA. Choose the model that matches both rules.

Bookify includes the valid empty-selection boundary while preserving the captured counting equations and enumeration ranges.