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How many solutions are there to the equation X₁ + x₂ + x3 = 21, if each x; is a positive integer? Use the method shown in Example 9.6.5 to answer this question. Start by thinking of the number 21 as divided into 21 individual items and the variables X₁, X₂, and x3 as three categories into which these items are placed. Since each x; is a ---Select--- integer, start by placing one item in each category and distribute the remaining items among the categories. The number of solutions to the equation that satisfy the given condition is the number of ways to place all the items into the categories. Thus, the answer is

How many solutions are there to the equation X₁ + x₂ + x3 = 21, if each x; is a positive integer? Use the method shown in Example 9.6.5 to answer this question. Start by thinking of the number 21 as divided into 21 individual items and the variables X₁, X₂, and x3 as three categories into which these items are placed. Since each x; is a ---Select--- integer, start by placing one item in each category and distribute the remaining items among the categories. The number of solutions to the equation that satisfy the given condition is the number of ways to place all the items into the categories. Thus, the answer is

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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How many solutions are there to the equation X₁ + x₂ + x3 = 21, if each x; is a positive integer? Use the method shown in Example 9.6.5 to answer this question. Start by thinking of the number 21 as divided into 21 individual items and the variables X₁, X2, and x3 as three categories into which these items are placed. Since each x; is a -Select--- integer, start by placing one item in each category and distribute the remaining items among the categories. The number of solutions to the equation that satisfy the given condition is the number of ways to place all the items into the categories. Thus, the answer is
Transcribed Image Text:How many solutions are there to the equation X₁ + x₂ + x3 = 21, if each x; is a positive integer? Use the method shown in Example 9.6.5 to answer this question. Start by thinking of the number 21 as divided into 21 individual items and the variables X₁, X2, and x3 as three categories into which these items are placed. Since each x; is a -Select--- integer, start by placing one item in each category and distribute the remaining items among the categories. The number of solutions to the equation that satisfy the given condition is the number of ways to place all the items into the categories. Thus, the answer is
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