Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations1h 31m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
10. Combinatorics & Probability
Factorials
Problem 59
Textbook Question
Textbook QuestionThe factorial of a positive integer n can be computed as a product. n! = 1 * 2 * 3 *. . . * n
Calculators and computers can evaluate factorials very quickly. Before the days of modern technology, mathematicians developed Stirling’s formula for approximating large factorials. The formula involves the irrational numbers p and e.
n! = √2πn * n^n * e^−n
As an example, the exact value of 5! is 120, and Stirling’s formula gives the approximation as 118.019168 with a graphing calculator. This is “off” by less than 2, an error of only 1.65%. Work Exercises 59–62 in order. Use a calculator to find the exact value of 10! and its approximation, using Stirling’s
formula.

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