Question

. An automobile license plate number issued by a certain state has 6 character positions. Each of the first 3 positions contains a single digit from 0 through 9. Each of the last 3 positions contains 1 of the 26 letters of the alphabet. Digits and letters of the alphabet can be repeated on a license plate. How many different such license plate numbers can be made

Answer 1

17,576,000

Explanation:

3 digits followed by 3 letters

Draw an underline character for each position with multiplication signs in between them.

_ × _ × _ × _ × _ × _

Now fill in each blank with the number of characters that can be used in that position. The first three blanks are used with digits, 0 through 9. There are 10 digits 0 through 9.

10 × 10 × 10 × _ × _ × _

For the last three blanks, each one gets a letter from A through Z. There are 26 letters to choose from fore each of the last three blanks.

10 × 10 × 10 × 26 × 26 × 26 = 17,576,000