   Chapter 9.5, Problem 12ES ### 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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# How many pairs of two distinct integers chosen from the set{1,2,3,…,101}have a sum that is even?

To determine

To find the numbers of pairs of two distinct integers chosen from the set {1,2,3,.....,101} have a sum that is even.

Explanation

Given information:

The given set is (1,2,3,.......101).

Concept used:

A sum of distinct integers can be even if both are even or both are odd

even+even=evenodd+odd=even

In the given set of 101 integers, the number of odd integers are 101+12=51, and the number of even integers are 10112=50.

Calculation:

Now, to attain an even sum of 2 distinct integers, we have to select the two integers from the set of 51 odd integers, or from the set of 50 even sddintegers

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