If a license plate consists of two letters followed by four digits, how many different licenses...

If a license plate consists of two letters followed by four digits, how many different licenses could be created having at least one letter or digit repeated.

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Expert Solution

A license plate consists of 2 letters, followed by 4 digits .

To find the number of license plates where at least one letter or digit is repeated

=Number of license plates where at least one letter or digit is repeated

=Total number of plates that can be created-Total number of plates where there are no repeatation.

(1) Now,Total number of plates that can be created

There are 26 letters for each of first two places and 10 digits for each of the next four.

So,the total number of license plates that can be created is

=26*26*10*10*10*10

=6760000

(2) Number of license plates where there are no repeatation.

In the first place,there can be 26 letters and in the second place there can be 25.

In the third place there can be 10 digits,and in the next three there can be 9,8 and 7 digits respectively.

So,total number of license plates in which there is no repeatation is

26*25*10*9*8*7

=3276000

So,our required number of license plates in which at least one letter or digit is repeated is

=6760000-3276000

=3484000.

orchestra answered 1 year ago

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