Evaluate the factorial expression. $$ \frac{107!}{105!} $$ $$ \frac{107!}{105!}=\square $$

Question

UpStudy AI · Accepted Answer

We start with the expression:

$$
\frac{107!}{105!}
$$

Recall that the factorial function is defined by:

$$
n! = n \times (n-1) \times (n-2) \times \cdots \times 1
$$

So, we write:

$$
107! = 107 \times 106 \times 105!
$$

Substitute this into the original expression:

$$
\frac{107!}{105!} = \frac{107 \times 106 \times 105!}{105!}
$$

Cancel out the $$105!$$ terms:

$$
\frac{107 \times 106 \times \cancel{105!}}{\cancel{105!}} = 107 \times 106
$$

Now, calculate the product:

$$
107 \times 106 = 107 \times (100 + 6) = 10700 + 642 = 11342
$$

Thus, the final answer is:

$$
\frac{107!}{105!} = 11342
$$
$$ \frac{107!}{105!} = 11342 $$

Evaluate the factorial expression. \( \frac{107!}{105!} \) \( \frac{107!}{105!}=\square \)