2. How mamy computer passwords are there that consist of 6 characters which can be either letters or digits if the first character has to be a letter? (There are 26 letters and 10 digits.)

To use the multiplication principle, we must break the process of determining how many possibilities there are into a series of decisions where no matter how the previous decision came out, there are always the same number of choices for the next decision.

The first decision is what the first character should be. Since there are 26 letters, there are 26 ways to choose the first character.

After the first character has been chosen, since these are computer passwords where the same letter may be used over again, there are still 26 letters from which to choose, but there are also 10 digits for a total of 36 possible characters.

After the second character has been chosen, there are also 36 possibilities for the third character.

After the third character has been chosen, there are also 36 possibilities for the fourth character.

After the fourth character has been chosen, there are also 36 possibilities for the fifth character.

After the fifth character has been chosen, there are also 36 possibilities for the sixth character.

The multiplication principle says to multiply these numbers

26x365 = 1,572,120,576