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: 18

Answer

a)256 b)56 c)219 d)70

Work Step by Step

a) Total possible outcomes = 2$\times$2...$\times$2 (8 times) = $2^{8}$ = 256. b) Exactly three heads = $C$(8,3) = 56 c) At least three heads = $C$(8,3) + $C$(8,4) + $C$(8,5) + $C$(8,6) + $C$(8,7) + $C$(8,8) = 56 + 70 + 56 + 28 + 8 + 1 = 219 d) Equal number of heads and tails i.e. exactly four heads = $C$(8,4) = 70
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