Chapter 12 - Data Analysis and Probability - 12-6 Permutations and Combinations - Practice and Problem-Solving Exercises - Page 754: 31

56

Use the formula of combination: $_{n}$C$_{r}$=$\frac{n!}{r!(n-r)!}$. Plug in 8 for N and 5 for R: $_{n}$C$_{r}$=$\frac{n!}{r!(n-r)!}$ $_{8}$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