Chapter 9.6, Problem 91E

To determine

To calculate: $P{}_{80}$ using graphing utility

Answer to Problem 91E

  $P{}_{80}=3.8360038806\times {10}^{139}$

Explanation of Solution

Given information: $P{}_{80}$

Formula needed: $P{}_r=\frac{n!}{\left(n-r\right)!}$

Calculation:First try to calculating using TI − 83 Plus (graphing utility)

Step 1: - Enter 100 in the calculator

  

Step 2: - Click on MATH button and press right arrow button four times.

  

Step 3: - Then, press 2

  

Step 4: - Enter 80

  

Step 5: - Output

  

The graphing calculator fail to calculate $P{}_{80}$ , do manually now

  $\begin{array}{l}P{}_{80}=\frac{100!}{\left(100-80\right)!}\\ P{}_{80}=\frac{100!}{20!}\\ P{}_{80}=\frac{100\cdot 99\cdot \mathrm{98...}\cdot 22\cdot 21\cdot 20!}{20!}\\ P{}_{80}=100\cdot 99\cdot \mathrm{98...}\cdot 22\cdot 21\\ P{}_{80}=3.8360038806\times {10}^{139}\end{array}$