   Chapter 9.6, Problem 13ES ### 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. y 1 + y 2 + y 2 + y 4 = 30 , each y i is an integer that is at least 2.

To determine

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

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

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:

The objective is to find the number of solutions to the equation y1+y2+y3+y4=30, for each yi2.

Let xi=yi2 for each i=1,2,3,4.

Then for each xi0.

y1+y2+y3+y4=30(x1+2)+(x2+2)+(x3+2)+(x4+2)=30y1+y2

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