   Chapter 9.6, Problem 14ES ### 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 10-14, find how many solutions there are to the given equation that satisfy the given condition. a + b + c + d + e = 500 , each of a , b , c , d , and e is an integer that is at least 10.

To determine

To find the number of solutions to the given equation that satisfy the given condition.

a+b+c+d+e=500, each of a,b,c,d and e is an integer that is at least 10.

Explanation

Given information:

y1+y2+y3+y4=30, each yi is an integer that is at least 2.

Concept used:

The number of r combinations with repetition allowed that can be selected from a set of n elements is:

(r+n1n1)

Calculation:

To find the number of solutions of a+b+c+d+e=500

a,b,c,d,e10

Let

x1=a10a=x1+10x2=b10b=x2+10x3=c10c=x3+10x4=d10d=x4+10x5=e10e=x5+10

a+b+c+d+e=500(x1+10)+(x2+10)+(x3+10)+(x4+10)+(x5+10)=500x1+x2+

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