College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 9, Counting and Probability - Section 9.1 - Counting - 9.1 Exercises - Page 658: 57



Work Step by Step

Let's number the children from oldest to youngest to make this problem easier. Then, we realize that this is just a sorting of the cones, $14!$. However, each type of cone is indistinguishable from another of its type. Therefore, we divide by repetitions, namely $3!$ for vanilla, $2!$ for chocolate, $4!$ for strawberry, and $5!$ for butterscotch. $\frac{14!}{3!*2!*4!*5!} = 2522520$
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