Questions: If a license plate consists of one of four characters followed by three letters and three digits, how many license plate combinations are possible assuming that repetition is permitted? Number of possible plates = (Type a whole number)

Solution Steps

To determine the number of possible license plate combinations, we need to consider each component of the plate separately. The plate consists of one of four shapes, followed by three alphabetic characters, and then three numeric characters. Since repetition is allowed, each alphabetic character can be any of the 26 letters, and each numeric character can be any of the 10 digits. Therefore, the total number of combinations is the product of the possibilities for each component.

The license plate consists of:

• 1 shape (from 4 options)
• 3 letters (each can be any of the 26 letters)
• 3 digits (each can be any of the 10 digits)

The total number of combinations can be calculated as follows:

• For the shape: \( 4 \)
• For the letters: \( 26^3 \)
• For the digits: \( 10^3 \)

The total number of possible license plates is given by the product of the combinations for each component: \[ \text{Total Combinations} = 4 \times 26^3 \times 10^3 \]

Calculating each part:

• \( 26^3 = 17576 \)
• \( 10^3 = 1000 \)

Thus, \[ \text{Total Combinations} = 4 \times 17576 \times 1000 = 70304000 \]

Final Answer