Statistics: Informed Decisions Using Data (4th Edition)

Published by Pearson
ISBN 10: 0321757270
ISBN 13: 978-0-32175-727-2

Chapter 5 - Review - Review Exercises - Page 316: 24

Answer

$1,217,566,350$ different samples.

Work Step by Step

The order in which the objects from a population are selected does not matter and no object can be selected more than once. Combination of 55 distinct objects taken 8 at a time: $_{55}C_8=\frac{55!}{8!(55-8)!}=\frac{55!}{8!\times47!}$ But, $55!=55\times54\times53\times52\times51\times50\times49\times48\times(47\times46\times45\times...\times3\times2\times1)=55\times54\times53\times52\times51\times50\times49\times48\times47!$ $_{55}C_8=\frac{55\times54\times53\times52\times51\times50\times49\times48\times47!}{8!\times47!}=\frac{55\times54\times53\times52\times51\times50\times49\times48}{8\times7\times6\times5\times4\times3\times2\times1}=\frac{49092275232000}{40320}=1,217,566,350$
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