Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 12 - Data Analysis and Probability - 12-6 Permutations and Combinations - Practice and Problem-Solving Exercises - Page 767: 45

Answer

$_{8}$C$_{5}$ is greater

Work Step by Step

You have $_{7}$C$_{4}$ and $_{8}$C$_{5}$.Solve to find out which is larger: A: $_{7}$C$_{4}$=$\frac{7!}{4!(7-4)!}$ -simplify like terms- $_{7}$C$_{4}$=$\frac{7!}{4! (3!)}$ -write using factorial- $_{7}$C$_{4}$=$\frac{7*6*5*4*3*2*1}{(4*3*2*1)(3*2*1)}$ -simplify- $_{7}$C$_{4}$=35 B: $_{8}$C$_{5}$=$\frac{8!}{5!(8-5)!}$ -simplify like terms- $_{8}$C$_{5}$=$\frac{8!}{5! (3!)}$ -write using factorial- $_{8}$C$_{5}$=$\frac{8*7*6*5*4*3*2*1}{(5*4*3*2*1)(3*2*1)}$ -simplify- $_{8}$C$_{5}$=56 $_{8}$C$_{5}$ is greater
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