Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 11 - Review Exercises - Page 842: 91



Work Step by Step

If we want to choose $k$ elements out of $n$ disregarding the order, not allowing repetition, we can do this in $_{n}C_k=\frac{n!}{(n-k)!k!}$ ways. The order doesn't matter here when selecting the people, thus we have to use combinations. We have $32$ people for $12$ spots, thus $_{32}C_{12}=\frac{32!}{(32-12)!12!}=225,792,840$
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