Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 6 - Section 6.3 - Permutations and Combinations - Exercises - Page 413: 17

Answer

$2^{100}$ - 5051 subsets with more than two elements.

Work Step by Step

Number of subsets with more than 2 elements = Total subsets - Subsets with at most 2 elements. Total subsets = $2^{100}$ Subsets with most 2 elements = $C$(100,2) + $C$(100,1) + $C$(100,0) = 4950 + 100 + 1 = 5051 Subsets with more than two elements = $2^{100}$ - 5051
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