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Mathematica > Constructing Lists >

Built-in Mathematica Symbol

Tuples

Tuples[list, n]
generates a list of all possible n-tuples of elements from list.

Tuples[{list₁, list₂, ...}]
generates a list of all possible tuples whose i

element is from list_i.

The elements of list are treated as distinct, so that Tuples[list, n] for a list of length k gives output of length kⁿ.

The order of elements in Tuples[list, n] is based on the order of elements in list, so that Tuples[{a₁, ..., a_k}, n] gives ${{a_1,a_1,…,a_1},{a_1,a_1,…,a_2},…,{a_k,a_k,…,a_k}}$ .

Tuples[list, {n₁, n₂, ...}] generates a list of all possible arrays of elements in list.

The object list need not have head List. The head at each level in the arrays generated by Tuples will be the same as the head of list.

All possible 3-tuples of 0 and 1:

The first element given is always picked first:

All ways of picking one element from each list: