1. **State the problem:** Simplify the factorial expression $$\frac{9! \times 8!}{11!}$$. 2. **Recall the factorial definition:** For any positive integer $n$, $n! = n \times (n-1) \times \cdots \times 1$. 3. **Rewrite the denominator using factorial properties:** $$11! = 11 \times 10 \times 9!$$ 4. **Substitute into the expression:** $$\frac{9! \times 8!}{11!} = \frac{9! \times 8!}{11 \times 10 \times 9!}$$ 5. **Cancel the common factor $9!$ in numerator and denominator:** $$= \frac{\cancel{9!} \times 8!}{11 \times 10 \times \cancel{9!}} = \frac{8!}{11 \times 10}$$ 6. **Calculate $8!$:** $$8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40320$$ 7. **Substitute and simplify:** $$\frac{40320}{11 \times 10} = \frac{40320}{110}$$ 8. **Simplify the fraction by dividing numerator and denominator by 10:** $$= \frac{\cancel{40320}^{4032}}{\cancel{110}^{11}} = \frac{4032}{11}$$ 9. **Final answer:** $$\boxed{\frac{4032}{11}}$$