Question

How many license plates can be made using 3 digits and 4 letters if repeated digits and letters are not allowed?

a) 258336000
b) 456976000
c) 217002240000
d) 1370928000
e) 775008000
f) None of the above

Answer 1

To find the number of license plates that can be made using 3 digits and 4 letters, we multiply the number of options for each part. The total number of license plates is 137,092,8000.

Step-by-step explanation:

To find the number of license plates that can be made using 3 digits and 4 letters, we need to calculate the number of options for each part and then multiply them together.

For the digits, we have 10 choices (0-9) for each digit, but since repeated digits are not allowed, the number of options decreases with each digit. So the number of options for the first digit is 10, for the second digit it is 9, and for the third digit it is 8.

Similarly, for the letters, we have 26 choices (A-Z) for each letter, but since repeated letters are not allowed, the number of options decreases with each letter. So the number of options for the first letter is 26, for the second letter it is 25, for the third letter it is 24, and for the fourth letter it is 23.

To find the total number of license plates, we multiply the number of options for each part. Therefore, the total number of license plates is 10 * 9 * 8 * 26 * 25 * 24 * 23 = 137,092,8000.