Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 11 - Probability and Statistics - 11-1 Permutations and Combinations - Practice and Problem-Solving Exercises - Page 678: 38

Answer

$56$ ways

Work Step by Step

There are 8 swimmers and the top 3 advance to the next round. Order does not matter here since so solve for $_{8}$C$_{3}$.using the formula $_nC_r=\dfrac{n!}{(r!(n-r)!)}$: $_8C_3=\dfrac{8!}{(3!(8-3)!)}$ $_8C_3=\dfrac{8!}{3!(5!)}$ $_8C_3=\dfrac{8*7*6*5*4*3*2*1}{(3*2*1)(5*4*3*2*1)}$ Simplify to get $C(8,3)=56$.
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