Suppose a license plate requires three letters ,followed by three digits.how many license plates are there if the letters are all different and the digits are all different
Do you consider on a license plat the O different from 0 (zero)? is l different from 1 (one)?
If so, you get 26*25*24*10*9*8
The answer to this question is 11232000. This is the correct answer.
To find the number of license plates, we need to consider the number of choices for each position on the license plate.
For the three letters, since they must all be different, we have 26 choices for the first letter, 25 choices for the second letter (since it must be different from the first letter), and 24 choices for the third letter (since it must be different from the first two letters). Therefore, the number of choices for the three letters is: 26 * 25 * 24 = 15,600.
For the three digits, since they must all be different, there are 10 choices for the first digit (0-9), 9 choices for the second digit (excluding the digit already chosen for the first position), and 8 choices for the third digit (excluding the digits already chosen for the first two positions). Therefore, the number of choices for the three digits is: 10 * 9 * 8 = 720.
To find the total number of license plates, we multiply the number of choices for the letters by the number of choices for the digits: 15,600 * 720 = 11,232,000.
So, there are 11,232,000 different license plates if the letters are all different and the digits are all different.