Chapter 13, Problem 18RE

To determine

To find: How many different plates are possible?

Answer to Problem 18RE

21600

Explanation of Solution

Given:

A license plate consists of 1 letter, excluding O and I, followed by a 4-digit number that cannot have a 0 in the lead position.

Calculation:

The generalized basic principle of counting.

We need to choose a license plate consisting of 1 letter, excluding O and I, followed by a 4-digit number that cannot have a 0 in the lead position.

First letter cannot be O or I.

Hence number of choices for 1^st letter is 24.

The second position cannot have digit 0.

Number of choices for each 2nd position is 9.

3^rd and 4^th digit can have 10 choices.

Therefore the number of options for the plate is $24*9*10*10 = 21600$.