Figure out total one-way permutations

Question

Check out the given sets:

1 => [
    a,
    b,
    c,
],
2 => [
    x,
    y,
    z,
],
3 => [
    i,
    o,
]

I need to adhere to my 1, 2, 3 order and determine the total permutations. So, here's the result:

a, x, i    a, x, o
b, x, i    b, x, o
c, x, i    c, x, o

a, y, i    a, y, o
b, y, i    b, y, o
c, y, i    c, y, o

a, z, i    a, z, o
b, z, i    b, z, o
c, z, i    c, z, o

...that's 18. How can I calculate this? At first, I thought (3 x 3) + (3 x 3) + (2 x 3) by that's obviously wrong. Clearly, maths is not my forte - so what am I missing? Thanks.

Answer 1

It's just $3\times 3\times 2$ - you have $3$ ways to make a choice from set 1, $3$ ways from set 2 and $2$ ways from set 3, and the three choices are independent so you just multiply the numbers.

This is the rule of product for combinatorics.