Question

1. Since 1963, the State of California has used the following rules for standard

car license plates
• Every license plate has the format ###AAA#, where # represents a numeral
0-9 and A represents a letter A-Z.
• The first and third letter positions cannot be I, O, or Q (to avoid
confusion with mumbers 1, 0).
How many license plates can the State of California issue that follow
these rules?

Answer 1

137,540,000

Explanation:

###AAA#

There are 10 digits from 0 to 9.

There are 26 letters from A to Z.

We apply the counting principle. We see the number of possible digits or letters than can be placed in each position, and then we multiply them together.

There are 10 digits for the first position.

###AAA#

10

There are 10 digits for the second position.

###AAA#

10 * 10

There are 10 digits for the third position.

###AAA#

10 * 10 * 10

There are 23 letters for the fourth position.

###AAA#

10 * 10 * 10 * 23

There are 26 letters for the fifth position.

###AAA#

10 * 10 * 10 * 23 * 26

There are 23 letters for the sixth position.

###AAA#

10 * 10 * 10 * 23 * 26 * 23

There are 10 digits for the seventh position.

###AAA#

10 * 10 * 10 * 23 * 26 * 23 * 10

Now we multiply all the numbers together.

10 * 10 * 10 * 23 * 26 * 23 * 10 = 137,540,000