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a set of license plates has three letters followed by 5 digits. (a) in how many ways can a license plate be made with three letters followed by 5 digits? (letters or digits may be repeated.)



Answer :

The license plate can be made in 1,757,600,000 ways

For the license plate, we need 3 letters out of 26 letters of the English alphabet and 5 digits out of 0-9

For the alphabet:

So, the first letter can be chosen in 26 ways

The second letter can be chosen in 26 ways

The third letter can be chosen in 26 ways

For the digits:

The first number can be chosen in 10 ways

The second number can be chosen in 10 ways

Similarly, the remaining three numbers can be chosen in 10 ways each

So, total ways = 26*26*26*10*10*10*10*10 = 1,757,600,000

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