   Chapter 9.4, Problem 29ES ### 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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# A certain collage class has 40 students. All the students in the class are known to be from 17 through 34 years of age. You want to make a bet that the class contains at least x students of the same age. How large can you make x and yet be sure to win your bet?

To determine

How large you can make x and yet to be sure to win your bet that is at least x students are of the same age.

Explanation

Given information:

There are 40 students in the college and they are from the age of 17 to 34 years of age.

Calculation:

Using the pigeonhole principle- the pigeonhole principle states that there must be at least one box which will contain two or more objects if n+1 objects are put in n boxes.

The pigeonhole principle can be expressed mathematically as nk, where n is the number of pigeons and k is the number of pigeonholes.

In the above problem n=40 and let us suppose k=18 which is in betweenthe age of 17 to 34 years

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