   Chapter 9.6, Problem 7ES ### 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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# Another way to count the nunibci ut nonricga-uve integral solmiorb to an equation of the form ¦«i *-«2 + •• ¦ * i» " m to reduce the pioblein lo one of finding ike number of n-tupies (r,. v;..... y„) with 0 £ vi * *i X ¦ ¦ ¦ * v. S m. The reduction ic%uli> from letting y,mXi+Xj + ¦•• + s,for each I ¦ 1.2.....n. Use Mi approach to derive a general formula for the number ot nunnegalive integral solution* to .«, + x, + -•• + *. — m.

To determine

To find another way to count the number of nonnegative integral solutions to an equation of the form x1+x2+.......+xn=m.

Explanation

Given information:

The objective is to determine the number of nonnegative integral solutions to

x1+x2+.......+xn=m.

Concept used:

Select n integers for the n tuples from the m integers (as0y1y2........ynm).

The order of integers does not matter. So, use a combinations.

Calculation:

The number of nonnegative integral solutions is.

( n+m1 n)=( n+m1)!n!( n+m1n)!=( n+m1)!n!( m1)!=( n+m1)( n+m2).....( n+1)n!n!( m1)( m2)....

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