How many license plates are possible consisting of 4 letters followed by 2 digits, if the first letter must be a C? Repetition is allowed.
To find the number of possible license plates that satisfy the given conditions, we can break down the problem into steps.
Step 1: Determine the number of options for the first letter.
Since the first letter must be a "C," there is only 1 option for this letter.
Step 2: Determine the number of options for each of the other three letters.
For each of the remaining three letters, repetition is allowed, so there are 26 options for each letter.
Step 3: Determine the number of options for each of the two digits.
For each digit, repetition is allowed, so there are 10 options for each digit.
Step 4: Calculate the total number of possible license plates.
Multiply the number of options from each step to get the total number of possible license plates:
1 (option for the first letter) * 26 (options for each of the three remaining letters) * 26 (options for the fourth letter) * 10 (options for each digit) * 10 (options for the second digit)
Total number of possible license plates = 1 * 26 * 26 * 10 * 10 = 676,000.
To calculate the number of possible license plates, we need to determine the number of choices for each character position.
Given that the first letter must be a "C", we have only one choice for the first position.
For the second, third, and fourth positions, we have 26 choices each, as there are 26 letters in the English alphabet.
For the fifth and sixth positions (digits), we have 10 choices each, as there are 10 possible digits (0-9).
To find the total number of possible license plates, we multiply the number of choices for each position:
1 choice for the first position * 26 choices for the second position * 26 choices for the third position * 26 choices for the fourth position * 10 choices for the fifth position * 10 choices for the sixth position.
Therefore, the total number of possible license plates is:
1 * 26 * 26 * 26 * 10 * 10 = 17,576,000.
So, there are 17,576,000 possible license plates consisting of 4 letters followed by 2 digits, if the first letter must be a "C" and repetition is allowed.