How many three-digit positive integers exist, all of whose digits are 2's and/or 5's?

Logic
Oct 9, 2018

#2**0 **

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.

\(2*2*2=8 \text{ integers}\)

TheXSquaredFactor
Oct 9, 2018