Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 12 - Counting and Probability - Section 12.2 Permutations and Combinations - 12.2 Assess Your Understanding - Page 875: 28


$\left\{\text{ab, ac, ad, ae, bc, bd, be, cd, ce, de}\right\}$ $C(5,2) = 10$

Work Step by Step

Order is not important in a combination. For example, $ab$ and $ba$ are considered as same combination. We list all possible arrangements taken 2 at a time from $a,b,c,d$ and $e$ and exclude arrangements with same objects but only different in order ( See definition of 'combination'): $\left\{\text{ab, ac, ad, ae, bc, bd, be, cd, ce, de}\right\}$. Use the formula $C(n, r)=\dfrac{n!}{(n-r)!\times r!}$: $C(5,2) \\= \dfrac{5!}{(5-2)!2!} \\= \dfrac{5!}{3!\times2!} \\= \frac{5\times4\times3!}{3!\times2!} \\ = 10$
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