Chapter 12 - Data Analysis and Probability - 12-6 Permutations and Combinations - Practice and Problem-Solving Exercises - Page 768: 61

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Use the formula of combination: $_{n}$C$_{r}$=$\frac{n!}{r!(n-r)!}$. Plug in 90 for N and 90 for R: $_{n}$C$_{r}$=$\frac{n!}{r!(n-r)!}$ $_{90}$C$_{90}$=$\frac{90!}{90!(90-90)!}$ -simplify like terms- $_{90}$C$_{90}$=$\frac{90!}{90! (0!)}$ -write using factorial- $_{90}$C$_{90}$=$\frac{90*89*88*87*..........3*2*1}{(90*89*88*87*...2*1)(1)}$ -simplify- $_{90}$C$_{90}$=1