Evaluate.
\[
\frac{17 !}{13 !}
\]
The solution is

Step 1 ：The factorial of a number n, denoted as n!, is the product of all positive integers less than or equal to n. For example, \(5! = 5 \times 4 \times 3 \times 2 \times 1 = 120\).

Step 2 ：In the given problem, we are asked to evaluate the expression \(\frac{17 !}{13 !}\). This can be simplified by cancelling out the common terms in the numerator and the denominator.

Step 3 ：The factorial of 17, \(17! = 17 \times 16 \times 15 \times 14 \times 13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\)

Step 4 ：The factorial of 13, \(13! = 13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\)

Step 5 ：We can see that the terms from 13 to 1 are common in both the numerator and the denominator. So, they can be cancelled out.

Step 6 ：This leaves us with \(\frac{17 !}{13 !} = 17 \times 16 \times 15 \times 14\)

Step 7 ：We can calculate this product to get the final answer.

Step 8 ：Final Answer: \(\boxed{57120}\)