College Algebra (10th Edition)

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

Chapter 10 - Test - Page 709: 15

Answer

See below.

Work Step by Step

We know that probability$=\frac{\text{number of favorable outcomes}}{\text{number of possible outcomes}}.$ The number of good outcomes is $1$. If we want to choose $k$ elements out of $n$ regarding the order, not allowing repetition, we can do this in $_{n}P_k=\frac{n!}{(n-k)!}$ ways. The order matters here when choosing the five balls, thus we have to use permutations. We have $10$ balls for $5$ spots, thus the number of all outcomes is: $_{10}P_{5}=\frac{10!}{(10-5)!}=30240$ Thus probability=$\frac{1}{30240}$
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