College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 10 - Section 10.2 - Permutations and Combinations - 10.2 Assess Your Understanding - Page 695: 33

Answer

$8$

Work Step by Step

Generalized Basic Counting Principle: Suppose there are $x$ experiments. If experiment $1$ can be performed in $n_{1}$ ways, experiment $2$ can be performed in $n_{2}$ ways, experiment $3$ can be performed in $n_{3}$ ways, and so on, then there are $n_{1} \times n_{2} \times n_{3} \times ... n_{x}$ ways of performing the $r$ experiments together. Since some digits can be repeated, there are $2$ choices for the first digit, $2$ choices for the second digit, and $2$ choices for the third digit as well. Therefore, $2 \times 2 \times 2 = 8$
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