Chapter 12 - Data Analysis and Probability - 12-6 Permutations and Combinations - Practice and Problem-Solving Exercises - Page 767: 53

56, combination

Use the formula of combination: $_{n}$C$_{r}$=$\frac{n!}{r!(n-r)!}$. Plug in 8 for N and 3 for R: $_{n}$C$_{r}$=$\frac{n!}{r!(n-r)!}$ $_{8}$C$_{3}$=$\frac{8!}{3!(8-3!)}$ -simplify like terms- $_{8}$C$_{3}$=$\frac{8!}{3! (5!)}$ -write using factorial- $_{8}$C$_{3}$=$\frac{8*7*6*5*4*3*2*1}{(3*2*1)(5*4*3*2*1)}$ -simplify- $_{8}$C$_{3}$=56