How many three-digit positive integers exist, all of whose digits are 2's and/or 5's?
Listing all the possible arrangements is one way to approach this problem; however, if I told you that this number has 10 or 100 digits, would you be as willing to write out all of them? I doubt it.
The first digit has two possibilities; it can either be a 2 or a 5.
The second digit has two possibilities; it can either be a 2 or a 5.
The third digit has two possibilities; it can either be a 2 or a 5.
\(2*2*2=8 \text{ integers}\)