Generate a N length vector from a M length list (permutation)

I have want to generate a 5-element vector:

A = [a1, a2, a3, a4, a5]

such that each element (a1...a5) could take on one of the three values [1, 2, 3];

There should be 3^5 number of outputs.

It should be easy but i have been trying for the last 90 minutes and got no luck.

[Stephen23]

"...such that each element (a1...a5) could take on one of the three values [1, 2, 3]"

"Just to clarify. [1, 2, 3, 4, 5] and [1, 2, 3, 5, 4] should be two separate outputs"

Your examples include values that are not in the list of values that you want. Confusing.

Is 5 permitted (as per your example) or not (as per your explanation) ?

[Yue Zhang]

Sorry about the confusion. I fixed my statement.

I guess what I'm trying to say is that this should be permutation instead of combination (sequence matters).

The key here is that the number of outputs should be 3^5. [1, 1, 1, 1, 2] and [1, 1, 1, 2, 1] should be two different outputs.

Neither 5 nor 4 is permitted.

[madhan ravi]

You still haven’t answered Stephen’s last question.

[Yue Zhang]

No. [1, 1, 1, 1, 2] and [1, 1, 1, 1, 2] should not be two different outputs. However [1, 1, 1, 1, 2] and [1, 1, 1, 2, 1] should.

Answer 1

[Walter Roberson]

[Ac{1:5}] = ndgrid(1:3);
result = cell2mat(cellfun(@(M) M(:), Ac, 'uniform', 0));

[Yue Zhang]

Thank you! This worked wonders!

Answer 2

[Andrei Bobrov]

out = fullfact(3*ones(1,5));