Use the Fundamental Counting Principle to solve the followin

Use the Fundamental Counting Principle to solve the following problem. In a plan for area codes, the first digit could be any number from 3 through 7, the second digit was either 0 or 1, and the third digit could be any except 0. With this plan, how many different area codes were possible? There were different codes possible.

Solution

With the first digit we have 5 options 3, 4, 5, 6, 7.

With the second digit we have 2 options 0 or 1.

With the third number we have 9 option 1, 2, 3, 4, 5, 6, 7, 8, 9

So you have to multiply all options that you have on each case:

5 x 2 x 9 = 90

There were 90 different codes possible.