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: 42



Work Step by Step

The number of arrangement of choosing $r$ objects out of $n$ distinct object $(r \leq n)$ is: $(a)$ If order matters, use permutation, i.e, $P(n, r)$. $(b)$ If order doesn't matter, use combination, i.e, $C(n, r)$. Order doesn't matter since once 3 professors are chosen for the committee, no matter how you arrange them, they are still the same 3 professors. Therefore, $C(8, 3) = \frac{P(8, 3)}{3!} = \frac{336}{6} = 56$
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