How many three digit numbers have an odd number integer in the tens spot?

Question:

Counting Principles

Combinatorics is an area of mathematics based mostly on counting. Counting is not always done simply by listing every possibility and then counting each one individually - in fact for many large problems this would take a long time. In many combinatorics problems, different techniques are used to count, such as using permutations, combinations, and simple logic. If one were to count how many four digit numbers start with a 9 and are even, every possibility could be listed, but this would take an unreasonable amount of time. Instead, consider the fact that the first digit only has one choice (9), the second and third digit can be any number so there are 10 choices for each (0 through 9), and the last digit must be even, so there are 5 choices (0,2,4,6,8). This results in a total of {eq}1\cdot 10\cdot 10 \cdot 5 = 500 {/eq} four digit numbers which begin with 9 and are also even.

Answer and Explanation: 1