Chapter 12 - Data Analysis and Probability - 12-6 Permutations and Combinations - Practice and Problem-Solving Exercises - Page 754: 33

28

Use the formula of combination: $_{n}$C$_{r}$=$\frac{n!}{r!(n-r)!}$. Plug in 8 for N and 6 for R: $_{n}$C$_{r}$=$\frac{n!}{r!(n-r)!}$ $_{8}$C$_{6}$=$\frac{8!}{6!(8-6)!}$ -simplify like terms- $_{8}$C$_{6}$=$\frac{8!}{6! (2!)}$ -write using factorial- $_{8}$C$_{6}$=$\frac{8*7*6*5*4*3*2*1}{(6*5*4*3*2*1)(2*1)}$ -simplify- $_{8}$C$_{6}$=28