Engineering Drawing Tree

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Probability - Computer & Switches?

A special-purpose computer has 2 switches, each can be set in 3 different positions, and 1 switch that can be set in 2 positions. In how many ways can the computer's switches be set?

This is a question from Miller & Freud's Probability and Statistics for Engineers 8th edition.

I've gotten an answer of 18 options. Is this correct? Other then drawing a tree diagram, is there another mathematical way to do this question?

Drawing tree diagram takes much of time.
the easier way is
to multiply the number of options in each switch
3 x 3 x 2 = 18
but anyway you are still right!

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