Chapter 12 - Data Analysis and Probability - 12-6 Permutations and Combinations - Practice and Problem-Solving Exercises - Page 766: 26

12144

This is a permutation problem since order and arrangement matter. Use the formula of permutation: $_{n}$P$_{r}$=$\frac{n!}{(n-r)!}$. Plug in 24 for N and 3 for R: $_{n}$P$_{r}$=$\frac{n!}{(n-r)!}$ $_{24}$P$_{3}$=$\frac{24!}{(24-3)!}$ -simplify- $_{24}$P$_{3}$=$\frac{24!}{21!}$ -write using factorial- $_{24}$P$_{3}$=$\frac{24*23*22*21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1}{21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1}$ -simplify- $_{24}$P$_{3}$=12144