1. A student's password for her school email consists of three characters.
The first character must be a lower-case letter. The second and third
characters must be single digits. If Caitlin wants to use the letter 'c' for
the first character, how many different passwords can she choose from?

Using the Fundamental Counting Theorem, it is found that she can choose 100 different passwords.

Fundamental counting theorem:

States that if there are n things, each with ways to be done, each thing independent of the other, the number of ways they can be done is:

In this problem:

Then:

She can choose 100 different passwords.

A similar problem is given at link

100

Step-by-step explanation:

the first digit can only be 1 thing: the letter c.

The second and third digits can make up number anywhere from 00 to 99. there are about 100 variations of the second and third digits, and 10 possibilities individually. multiply the 1 from the first digit and the 10 from the second and the 10 from the third to get 100.