The value of the expression $\frac{3!}{9!} + \frac{10!}{10!} + \frac{1}{8!}$ is approximately 1.00004.

Would you like more details or clarifications? Here are five related questions to explore:

1. What is a factorial and how is it calculated?
2. How does the factorial function grow with larger numbers?
3. Can you express factorial terms in simplified ratios?
4. What are the common uses of factorials in probability and combinatorics?
5. How would the result change if we altered one of the factorials, say $\frac{2!}{9!}$?

Tip: Factorials grow extremely fast! Even a small increase in the number can drastically change the value.