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If I define 3 variables that can be either set to the values high, medium, or low, like this:

High High High, or

High High Low, or

High Low High, or

High High Medium

And so on,

How many combinations can there be in total?

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    If order matters, $3^3 = 27$ – 2017-02-15
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    Order matters, so $3^3$ possibilities – 2017-02-15

2 Answers 2

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Hint:

It can clearly be seen from your examples that: repetition is allowed and order matters.

Taking these two factors into account, we have three possibilities for each place: high, medium and low. Each of the three places have these options. So, a total of $3\times 3\times 3 = 3^3 = 27$. Hope it helps.

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    Thanks alot for the explanation. I made a drawing before I wrote the question and your answer was the same as mine, but now I understand how to calculate it. – 2017-02-15
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You have $3$ possibilities (High, medium, low) for each of the three variables. So, in total, you have $3^3=27$ possibilities.