Chapter 15.5, Problem 14WE

To determine

To calculate: The number of license plates of 4 symbols with two letters and two digits.

Answer to Problem 14WE

The number of license plates of 4 symbols with two letters and two digitsare $405600$ .

Explanation of Solution

Given information:

The license plates of 4 symbols that include both letters and symbols with two letters and two digits is to be formed.

Formula used:

Fundamental counting principle states that if there are m ways to make a selection and n ways to make a second selection then there are $m\times n$ number of ways in which two selection can be made.

Calculation:

Consider the provided information that license plates of 4 symbols that include both letters and symbols with two letters and two digits is to be formed.

There are 26 letters and 10 digits from 0 to 9.

Let 4-symbol license plate be $\boxed{}\boxed{}\boxed{}\boxed{}$ .

First two boxes have 26 possibilities each as 26 letters are there and the last two boxes has 10 ways in which it can be filled.

  $\boxed{26}\boxed{26}\boxed{10}\boxed{10}$

Recall that Fundamental counting principle states that if there are m ways to make a selection and n ways to make a second selection then there are $m\times n$ number of ways in which two selection can be made.

Therefore, the number of ways to select are,

  $26\times 26\times 10\times 10=67600$

Total number of ways in which this can be done are 6 as first 2 letters then 2 digits, 2 digits then 2 letters, 1 letter 1 digit 1 letter 1 digit and each way listed above has further 2 more change of position possible has it has 2 letters and 2 digits.

  $67600\times 6=405600$

Thus, number of license plates of 4 symbols with two letters and two digits are $405600$ .