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: 76

Answer

Sample answer: "A committee of five students, out of a class with ten female and seven male students, must be formed so that there will be 3 female and 2 male students on the committee. How many different committees can be formed?"

Work Step by Step

We need a problem with a sequence of selections: 1. Selection of several items from the first group 2. Selection of several items from the second group Each individual selection needs the combination formula, and the sequence involves applying the Fundamental Counting Principle Sample answer: "A committee of five students, out of a class with ten female and seven male students, must be formed so that there will be 3 female and 2 male students on the committee. How many different committees can be formed?" (Step 1: choosing female members ... in ${}_{10}C_{3}$ ways Step 2: choosing male members ... in ${}_{7}C_{2}$ ways, By FCP, total = ${}_{10}C_{3}\cdot {}_{7}C_{2}$ ways)
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