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So, I'm a little confused on how to figure this out.

I am designing some props, I have 6 groups of design elements, 5 of them with 8 variations, and the last one with 2 variations.

I am trying to figure out how many different permutations or combinations (not sure which one is the correct term in this case) there are if only 1 element from each of the groups is chosen.

If I am remembering my math correctly (I've been out of school for 10 years now), to figure this out, I would need to take the number of elements of a particular group, and multiply that by the number of elements in each subsequent group. So, A * B * C * D * E * F, or, in this case, 8*8*8*8*8*2 to get 65,536.

Am I doing this correctly?

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8 ways to choose one item from the first design group, and for each of those ways, there are 8 ways to choose one item from the second design group, and for each of those ways, there are ... and finally 2 ways to choose an item from the last group.

Yes, use multiplication as you've specified it.

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