Find the possible nuber of license plates consisting of 2 letters followed by 4 digits if digits can be repeated but letters can not

a. 3,276,000
b. 3,407,040
c. 6,500,000
d. 6,760,000

I thought 26*24*24*23*22*21*20 etc/9 but that wasn't right and its just really confusing

the two letters at the front cannot be repeated, so that is 26*25

there are one 10 of digits in each of the
next 4 places, with the digits repeated, so that would be 10*10*10*10

no of ways = 26*25*10*10*10*10 = 6500000

I don't understand at all how you came up with 26*24*24*23*22*21*20

Yes the answer 6500000 is correct

To find the possible number of license plates consisting of 2 letters followed by 4 digits, you can break down the problem into separate steps.

Step 1: Calculate the number of possibilities for the first letter.
Since letters cannot be repeated, there are 26 options for the first letter.

Step 2: Calculate the number of possibilities for the second letter.
Since letters cannot be repeated, there are 25 options for the second letter (one less than the total number of letters).

Step 3: Calculate the number of possibilities for each digit.
Since digits can be repeated, there are 10 options for each of the four digits.

Step 4: Multiply the results from steps 1, 2, and 3 together to get the total number of possibilities.
Total possibilities = (Number of possibilities for first letter) * (Number of possibilities for second letter) * (Number of possibilities for each digit)
Total possibilities = 26 * 25 * 10 * 10 * 10 * 10
Total possibilities = 6,500,000

Therefore, the correct answer is option c) 6,500,000.

To find the possible number of license plates consisting of 2 letters followed by 4 digits, we can break down the problem into two separate parts: counting the possibilities for the letters and counting the possibilities for the digits.

1. Counting the possibilities for the letters:
Since there are 26 letters in the English alphabet and each letter can only be used once, we have 26 choices for the first letter and 25 choices for the second letter. So, the total number of possibilities for the letters is 26 * 25 = 650.

2. Counting the possibilities for the digits:
Since digits can be repeated, we have 10 choices for each of the four digits. Therefore, the total number of possibilities for the digits is 10 * 10 * 10 * 10 = 10,000.

Now, to find the total number of license plates, we simply multiply the possibilities for the letters by the possibilities for the digits:

Total number of license plates = Possibilities for letters * Possibilities for digits
= 650 * 10,000
= 6,500,000

Therefore, the correct answer is option c. 6,500,000.