## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 11 - Counting Methods and Probability Theory - 11.3 Combinations - Exercise Set 11.3 - Page 709: 80

1365 samples

#### Work Step by Step

A sample implies that the order of selecting its contents in unimportant. We work with combinations. The sample with no defective phones has been chosen in a way that: (1) 4 phones were chosen from the 15 working phones (2) 0 phones were chosen from the 5 defective phones Total: ${}_{15}C_{4}\displaystyle \cdot {}_{5}C_{0}=\frac{15!}{(15-4)!4!}\times\frac{5!}{(5-0)!0!}$ ... by definition, $0!=1$... $=\displaystyle \frac{15\times 14\times 13\times 12}{1\times 2\times 3\times 4}\cdot 1$ $=1365$

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