You are going to order a personalized license plate. How many possible choices do you have if yyou want the license plate to be four letters, none of which repeat, followed by a number?
number of plates = 26*25*24*23*10 = ....
The correct answer is 3588000
To determine the number of possible choices for a personalized license plate with four letters (none of which repeat) followed by a number, we can break down the problem into two parts: selecting the letters and selecting the number.
1. Selecting the letters:
Since none of the letters can repeat, we will choose them one by one.
For the first letter, we have 26 options (A to Z).
For the second letter, we have 25 options left (after excluding the first letter).
For the third letter, we have 24 options remaining.
For the fourth letter, we have 23 options left.
To calculate the total number of possible choices for the letters, we need to multiply these numbers together:
26 * 25 * 24 * 23 = 358,800 possible choices for the four letters.
2. Selecting the number:
Assuming the number can be any digit from 0 to 9 (inclusive), we have 10 options.
Now, to find the total number of possible choices for the license plate, we multiply the number of choices for the letters by the number of choices for the number:
358,800 * 10 = 3,588,000 possible choices.
Therefore, you have 3,588,000 possible choices for the personalized license plate with four unique letters followed by a number.