Chapter 12.6, Problem 1P

A six-character license plate number can begin with any two letters and end with four one-digit numbers.

1. How many possible choices are there for the first two characters? For the last four characters?
2. How many different six-character license plate numbers are possible?

To determine

Find the number of possible choices for the first two characters , for the last four characters.

Answer to Problem 1P

Possible number of choices for the first two characters = 676

Possible number of choices for the last four characters = 10,000

Explanation of Solution

Given:

A six-character license plate number can begin with any two letters and end with four one-digit numbers.

Calculation:

Since all the choices are possible , also repeating of characters are possible .

First two characters needs to be filled by letters .There are 26 letters .

Hence there are $26\times 26=676$ possible choices for the first two characters.

Last four characters needs to be filled by digits − 0,1,2,3,4,5,6,7,8,9 − So, 10 choices .

Hence there are $10\times 10\times 10\times 10=10000$ possible choices for the last four characters.

To determine

Find the possible number of different six-character license plates.

Answer to Problem 1P

  $6,760,000$

Explanation of Solution

Given:

A six-character license plate number can begin with any two letters and end with four one-digit numbers.

Calculation:

From part (a),

Possible number of choices for the first two characters = 676

Possible number of choices for the last four characters = 10,000

Hence, the possible number of different six-character license plates is $676\times 10,000=6,760,000$ .