Chapter 12 - Data Analysis and Probability - 12-6 Permutations and Combinations - Practice and Problem-Solving Exercises - Page 754: 34

21

Use the formula of combination: $_{n}$C$_{r}$=$\frac{n!}{r!(n-r)!}$. Plug in 7 for N and 5 for R: $_{n}$C$_{r}$=$\frac{n!}{r!(n-r)!}$ $_{7}$C$_{5}$=$\frac{7!}{5!(7-5)!}$ -simplify like terms- $_{7}$C$_{5}$=$\frac{7!}{5! (2!)}$ -write using factorial- $_{7}$C$_{5}$=$\frac{7*6*5*4*3*2*1}{(5*4*3*2*1)(2*1)}$ -simplify- $_{7}$C$_{5}$=21