Question

select the correct answer.
a state license plate consists of three letters followed by three digits. if repetition is allowed, how many different license plates are possible?
a. 17,576,000
b. 12,812,904
c. 11,232,000
d. 7,862,400

Explanation:

Step1: Calculate number of letter combinations

There are 26 letters in the alphabet, and for each of the three letter positions, we have 26 choices (since repetition is allowed). So the number of ways to choose the three letters is $26\times26\times26 = 26^3$.
Calculating $26^3$: $26\times26 = 676$, then $676\times26 = 17576$.

Step2: Calculate number of digit combinations

There are 10 digits (0 - 9), and for each of the three digit positions, we have 10 choices (repetition allowed). So the number of ways to choose the three digits is $10\times10\times10 = 10^3=1000$.

Step3: Calculate total number of license plates

To find the total number of different license plates, we multiply the number of letter combinations by the number of digit combinations. So that's $17576\times1000 = 17576000$.

Answer:

A. 17,576,000