What percent of these integers contain only odd digits?

Question

There are 900 3-digit integers, the integers between 100 and 999, inclusive.

Answer 1

Solution.

Let abc be any 3-digit integer containing only odd digits. Since each of the digits a, b, and c is odd, it can only be one of the 5 digits 1, 3, 5, 7, and 9, so there are 5 ways to assign a value to each of a, b, and c. By the Multiplication Principle, there are

5 × 5 × 5 = 125

ways to generate a 3-digit integers containing only odd digits. There are 900 3 digit integers, between 100 and 999, inclusive. Therefore, the required percentage is

125 ⁄ 900 = 5 ⁄ 36 ≈ 13.9%

Answer: Approximately 13.9% of the 3-digit integers contain only odd digits.