Question

A state requires that all boat licenses consist of the letter A or M followed by any five digits. What is the number of groups of letters and numbers available for boat licenses?

Answer 1

200000

Explanation:

There are two choices for the letter, followed by ten choices of a digit for each of the next five slots. Thus, there are 2·10^5 = 200000 combinations.

Answer 2

200000

Explanation:

The boat licenses are strings of six elements. Let's count the number of ways of constructing such string with the given conditions.

There are 2 ways of choosing the first character of the string (A or M). The second character can be any digit, so there are 10 possible choices. The third character is also any digit, so it can be chosen in 10 ways. Similarly, the fourth character can be chosen in 10 ways, and the fifth character can be chosen in 10 ways.

By the product rule there are 2×10×10×10×10×10=2×10^5=200000 ways to choose all the characters. Every choice of characters becomes a unique string (boat license) thus the number of avaliable boat licenses is 200000.s