A license plate in a particular state consists of 5 characters. The first 4 characters are made up using the digits 0-9, but the first character cannot be a zero. The remaining characters are letters. No characters can be repeated. How many different license plates are available?
9 char for the 1st position
9 for the 2nd
8 for the 3rd
7 for the 4th
26 for the 5th
9 * 9 * 8 * 7 * 26
To solve this problem, we can break it down into two parts:
1. Finding the number of options for the first 4 characters.
2. Finding the number of options for the last character.
1. Finding the number of options for the first 4 characters:
Since the first character cannot be zero, we have 9 options (digits 1-9) for the first character. The remaining three characters can be any of the 10 digits (0-9) excluding the ones already used. So, for the second character, we have 9 options, for the third character, we have 8 options, and for the fourth character, we have 7 options. Therefore, the total number of options for the first 4 characters is 9 * 9 * 8 * 7 = 4,536.
2. Finding the number of options for the last character:
The last character is a letter, and no characters can be repeated. There are 26 letters in the English alphabet. Since we have already used 4 characters, there are 26 - 4 = 22 letters remaining. So, the number of options for the last character is 22.
Now, to find the total number of different license plates available, we multiply the number of options for the first 4 characters by the number of options for the last character:
Total number of license plates = 4,536 * 22 = 99,792.
Therefore, there are 99,792 different license plates available in this particular state.