How many three-digit positive integers exist, all of whose digits are 2's and/or 5's?
I need to count the number of ways to form a three-digit number using only the digits 2 and 5. I can think of each digit as a choice between two options: 2 or 5. So, for the first digit, I have two choices: 2 or 5. For the second digit, I also have two choices: 2 or 5. And for the third digit, I again have two choices: 2 or 5. Since each choice is independent of the others, I can multiply the number of choices for each digit to get the total number of choices for the whole number. So, the total number of choices is 2 * 2 * 2, which is 2^3, which is 8. Therefore, there are 8 three-digit positive integers that consist only of 2's and/or 5's. 