Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 12 - Data Analysis and Probability - 12-6 Permutations and Combinations - Practice and Problem-Solving Exercises - Page 755: 46


45 line segments are needed .

Work Step by Step

There are 10 points for figure 2.Use the formula of combination: $_{n}$C$_{r}$=$\frac{n!}{r!(n-r)!}$. Plug in 10 for N and 2 for R: $_{n}$C$_{r}$=$\frac{n!}{r!(n-r)!}$ $_{10}$C$_{2}$=$\frac{10!}{2!(10-2)!}$ -simplify like terms- $_{10}$C$_{2}$=$\frac{10!}{2! (8!)}$ -write using factorial- $_{10}$C$_{2}$=$\frac{10*9*8*7*6*5*4*3*2*1}{(2*1)(8*7*6*5*4*3*2*1)}$ -simplify- $_{10}$C$_{2}$=45 We need 45 line segments to join each point for figure 2.
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