Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 11 - Counting Methods and Probability Theory - 11.3 Combinations - Exercise Set 11.3 - Page 708: 60



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 $_{n}C_k=\frac{n!}{k!(n-k)!}$ ways. Hence here because we have $7$ spots for $2$ people, $_{7}C_2=\frac{7!}{2!(7-2)!}=7\cdot6/2=21$
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