A license plate consists of 3 letters followed by 2 digits. How many license plates are possible if the 1st letter cannot be I nor O, the 1st digit cannot be 0, and no letters or digits may repeat?
a) 1,080,000
b) 1,166,400
c) 1,757,600
d) 1,460,160
e) 1,152,000
To find the number of possible license plates, we need to count the number of choices for each position in the license plate.
First, let's consider the choices for the first letter. Since the letter cannot be I or O, there are 24 options (26 letters in the alphabet minus 2 restricted letters).
Next, let's consider the choices for the second letter. Since no letters can repeat, there are 25 options available (26 letters minus the 1 letter already chosen for the first position).
Similarly, for the third letter, there are 24 options available (26 letters minus 2 letters already chosen).
Now, let's consider the choices for the first digit. Since the digit cannot be 0, there are 9 options available (Digits from 1 to 9).
Finally, for the second digit, there are 8 options available (Digits from 0 to 9 excluding the one already chosen for the first position).
To find the total number of possibilities, multiply the number of choices for each position: 24 * 25 * 24 * 9 * 8 = 1,152,000.
Therefore, the correct answer is (e) 1,152,000.