   Chapter 9.3, Problem 6ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# In a certain stale, all license plain consist of from lour to six symbols chosen irom the 2b uppercase letters of the Roman alphabet together with (he ten digits 0-9.a. How many license plates are possible if repetition of symbols is allowed? b. How many license plates do not contain any repealed sy mhols? C. How many license plates have at least one repeated symbol? d- What is the probabilility that a license plate chosen at random has at least one repealed symnbol?

To determine

(a)

The total number of license plates with four to five digits including repetitions out of 26 letters and 10 digits.

Explanation

Given information:

A license plate of this state contains only four to five digits from 26 roman uppercase letters and 10 digits from 0 to 9.

Formula used:

If we have to select m number of digits from n number of digits with repetitions,

The total number of combinations=nm

Calculation:

Let’s consider the count of license plates with four digits.

With formula above, we can observe that n=36,m=4.

Hence,

The total number of combinations=nm=364=1,679,616

Also, for the five digits in the license plat

To determine

(b)

The number of license plates do not contain any repetitions.

To determine

(c)

The count of license plates that have at least one repeated symbol.

To determine

(d)

The probability of choosing a random license plate that has at least one repetition.

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