Question 137019: The license plates for a certain state consist of two letters followed by a five - digit number such that the first digit of the number is not zero. An example for two letters and four digits is PK-2446. (If the problem has no solution, enter NONE in the answer box.)
(a) How many different license plates can be produced?
(b) How many different plates do not have a repeated letter?
(c) How many plates do not have any repeated digits in the number part of the plate?
(d) How many plates do not have a repeated letter and also do not have any repeated digits?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The license plates for a certain state consist of two letters followed by a five - digit number such that the first digit of the number is not zero. An example for two letters and four digits is PK-2446. (If the problem has no solution, enter NONE in the answer box.)
(a) How many different license plates can be produced?
# = 26*26*9*10^4 =60,840,000
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(b) How many different plates do not have a repeated letter?
# = 26*25*9*10^4
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(c) How many plates do not have any repeated digits in the number part of the plate?
# = 26^2*9*9*8*7
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(d) How many plates do not have a repeated letter and also do not have any repeated digits?
# = 26*26*9*9*8*7
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Cheers,
Stan H.
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