How many license plates can be formed if every license plate has 2 different letters (A through Z) followed by 2 different one digit (0-9) numbers?
I need to count how many ways I can choose 2 different letters and 2 different numbers. For the first letter, I have 26 options. For the second letter, I have 25 options, since I can't repeat the first letter. So, for the two letters, I have 26 times 25 ways to choose them. For the first number, I have 10 options, since any digit from 0 to 9 is allowed. For the second number, I have 9 options, since I can't repeat the first number. So, for the two numbers, I have 10 times 9 ways to choose them. To get the total number of license plates, I need to multiply the number of ways to choose the letters and the number of ways to choose the numbers. This gives me 26 times 25 times 10 times 9, which is 58,500. 