Questions: Evaluate the expression. If the answer is not an integer, round to four decimal places. 400! / 398! Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The value is an integer, 400! / 398! = . (Type an integer.) B. The value is not an integer, 400! / 398! = . (Round to four decimal places as needed.)

Evaluate the expression. If the answer is not an integer, round to four decimal places.

400! / 398!

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The value is an integer, 400! / 398! = .
(Type an integer.)
B. The value is not an integer, 400! / 398! = .
(Round to four decimal places as needed.)

Transcript text: Evaluate the expression. If the answer is not an integer, round to four decimal places. \[ \frac{400!}{398!} \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The value is an integer, $\frac{400!}{398!}=$ $\square$ . (Type an integer.) B. The value is not an integer, $\frac{400!}{398!}=$ $\square$ . (Round to four decimal places as needed.)

Solution

Solution Steps

To evaluate the expression $\frac{400!}{398!}$, we can simplify it by canceling out the common factorial terms. Specifically, $\frac{400!}{398!} = 400 \times 399$ because the $398!$ in the numerator and denominator cancel each other out. This results in a simple multiplication of the two remaining terms.

Step 1: Simplifying the Expression

To evaluate the expression $\frac{400!}{398!}$, we can simplify it by canceling the common factorial terms. This gives us: \[ \frac{400!}{398!} = 400 \times 399 \]

Step 2: Performing the Multiplication

Next, we calculate the product: \[ 400 \times 399 = 159600 \]