I have 3 categories. Each of these categories has three options.
Category 1 options: A, B, C
Category 2 options: D, E, F
Category 3 options: G, H, I
So a permutation of these may look like this: A E H
I am trying to find the number of permutations with these categories.
This looks like a special kind of permutations problem and I am not sure how to approach it, can anyone help please?
There are $3$ ways to choose the letter from each category, and then $3!$ ways of permuting them, giving a total of $$3^3\times 3!=162$$ ways.