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 766: 39



Work Step by Step

We have to find the combinations of 30 fabrics chosen 5 at a time. Use the formula of combination: $_{n}$C$_{r}$=$\frac{n!}{r!(n-r)!}$. Plug in 30 for N and 5 for R: $_{n}$C$_{r}$=$\frac{n!}{r!(n-r)!}$ $_{30}$C$_{5}$=$\frac{30!}{5!(30-5)!}$ -simplify like terms- $_{30}$C$_{5}$=$\frac{30!}{5! (25!)}$ -write using factorial- $_{30}$C$_{5}$=$\frac{30*29*28*27*26*25*..........9*8*7*6*5*4*3*2*1}{(5*4*3*2*1)(25*24*23*22*21*.........5*4*3*2*1)}$ -simplify- $_{30}$C$_{5}$=142506
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