Question

Suppose we are making license plates of the form l1l2l3 ???? d1d2d3 where l1; l2; l3 are capital letters in the English alphabet and d1; d2; d3 are decimal digits (i.e., elements of the set f0; 1; 2; 3; 4; 5; 6; 7; 8; 9g) subject to the restriction that at least one digit is nonzero and at least one letter is K. How many license plates can we make?

Answer 1

To calculate the number of license plates that can be made, we consider the restrictions on letters and digits. There are 25 options for the first letter, 26 options for the second and third letters, and 9 options for each digit. Multiplying these options together gives a total of 1,408,350 possible license plates.

Step-by-step explanation:

To calculate the number of license plates that can be made, we need to consider the restrictions given. Let's break it down:

1. First, let's consider the letters. There are 26 capital letters in the English alphabet. Since at least one letter must be K, we have 25 options for the first letter and 26 options for the second and third letters.
2. Next, let's consider the digits. There are 10 decimal digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). Since at least one digit must be nonzero, we have 9 options for each of the three digits.
3. Now, we can multiply the number of options for the letters and the digits together. So, the total number of license plates that can be made is 25 x 26 x 26 x 9 x 9 x 9 = 1,408,350