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Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

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BuyFindarrow_forward

Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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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 determine

(a)

To find number of license plates are possible if repetition of symbols is allowed.

Explanation

Given information:

Number is A to Z which is 26 and digit is 0 to 9.

Concept used:

A license that do not contain any repeated symbol.

Calculation:

If repetition is allowed and license plates consist four symbols out of 26 letter and 10 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 36 in 36 ways, similarly others three can be chosen in 36 ways, therefore by multiplication principle there are

36363636=364=1679616

License plates are possible with four symbols

To determine

(b)

To find how many different license plates can the state produce.

To determine

(c)

To find the number of license plates have at least one repeated symbol.

To determine

(c)

To find the probability that a license plate chosen at random has a repeated symbol.

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