1
$\begingroup$

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?

$\endgroup$
2
  • $\begingroup$ If order matters, $3^3 = 27$ $\endgroup$
    – joeb
    Feb 15, 2017 at 12:37
  • $\begingroup$ Order matters, so $3^3$ possibilities $\endgroup$ Feb 15, 2017 at 12:39

2 Answers 2

1
$\begingroup$

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.

$\endgroup$
1
  • $\begingroup$ 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. $\endgroup$ Feb 15, 2017 at 12:42
1
$\begingroup$

You have $3$ possibilities (High, medium, low) for each of the three variables. So, in total, you have $3^3=27$ possibilities.

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .