combination GRE problem 25

Question

An appliance's model number consists of three alphanumeric characters. The first character must be one of 24 permissible letters of the alphabet. The next character is numeric, a digit from 1 to 9. The last character is also numeric, a digit from 0 to 9. how many distinct model numbers are possible?

Answer 1

The best way to understand the solution is to draw a tree diagram. For each of the 24 letters you choose first, there are 9 possible numbers giving $24 \times 9$ different options. Now for each one of these $24 \times 9$ options of (letters followed by a number) there are 10 ways to choose the last the last number. Giving a total of $24 \times 9 \times 10$ options in total.

Answer 2

If I am reading this correctly, this would mean there are

1. $24$ ways to choose the alphabet of letters.
2. $9$ ways to choose your numbers (count with your fingers).
3. $10$ ways to choose your numbers.

So by the Fundamental Counting Principle, there are precisely $24*9*10 = 2160$ combinations.