In a certain country license plates consist of zeroor one digit followed by four or five uppercase letrers from the Roman alphabet.
(a) How many different license plates can the country produce?
(b) How many license plates have no repeated letter?
(c) How many license plates have at least one repeated letter?
(d) What is the probability that a license plate has a repeated letter?
To find number of license plates are possible if repetition of symbols is allowed.
Number is A to Z which is 26 and digit is 0 to 9.
A license that do not contain any repeated symbol.
If repetition is allowed and license plates consist four symbols out of letter and digits, these are four step operation; chose the first symbol, then second symbol, then third symbol and then the fourth.
Thus first symbol can be chosen out of in ways, similarly others three can be chosen in ways, therefore by multiplication principle there are
License plates are possible with four symbols
To find how many different license plates can the state produce.
To find the number of license plates have at least one repeated symbol.
To find the probability that a license plate chosen at random has a repeated symbol.
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