Calculate the value of the following factorial expression. Write the exact answer. Do not round.110!108!

To calculate the value of the factorial expression $\frac{110!}{108!}$, we can simplify it first.

1. Break Down the Problem

We are tasked with simplifying the expression $\frac{110!}{108!}$.

2. Relevant Concepts

Recall the definition of factorial:

• $n! = n \times (n-1) \times (n-2) \times \ldots \times 1$

Using this, we find: $110! = 110 \times 109 \times 108!$

3. Analysis and Detail

Substituting the expression for $110!$ into our original expression: $\frac{110!}{108!} = \frac{110 \times 109 \times 108!}{108!}$ When we simplify this, the $108!$ in the numerator and denominator cancel out: $\frac{110 \times 109 \times \cancel{108!}}{\cancel{108!}} = 110 \times 109$

Now we perform the multiplication: $110 \times 109 = 11990$

4. Verify and Summarize

The calculations show $110 \times 109 = 11990$. We did not round any numbers as they are all integers.

Final Answer

The exact value of $\frac{110!}{108!}$ is $11990$.