How many different three-digit numbers can you make using only the odd digits? (You can use each digit as many times as you like).
Solution:
It is possible to solve this problem by listing all the possible numbers but it would take a long time. Instead it is best to think about the possible combinations. There are five odd digits (1, 3, 5, 7, and 9). This means that there are five possibilities for the first digit of the number. For each of these there are five possibilities for the second digit, making a total of 5 x 5, or 25 possibilities for the first two digits. For each of these 25 possibilities there are five choices for the final digit. 25 x 5 = 125.
There are a total of 5 x 5 x 5, or 125 three digit numbers you can make using only odd digits.