Question: Evaluate the expression. If the answer is not an integer, round to four decimal places. 16! 2!(16 -…

Evaluate the expression. If the answer is not an integer, round to four decimal places. 16! 2!(16 - 2)! … Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The value is an integer, 16! = (Type an integer.) 2!(16 - 2)! B. The value is not an integer, 16! = (Round to four decimal places as needed.) 2!(16 - 2)!

Solution

We need to evaluate the expression: \[ \frac{16!}{2!(16-2)!} \] Start by simplifying the expression inside the factorial: \[ 16 - 2 = 14 \] Substitute back into the expression: \[ \frac{16!}{2! \cdot 14!} \] Break down the factorials: \[ 16! = 16 \times 15 \times 14! \] Substitute and simplify: \[ \frac{16 \times 15 \times 14!}{2! \cdot 14!} \] Cancel out \(14!\) from the numerator and the denominator: \[ \frac{16 \times 15}{2!} \] Calculate \(2!\): \[ 2! = 2 \] Substitute and simplify: \[ \frac{16 \times 15}{2} = \frac{240}{2} = 120 \] The value is an integer, so the answer is: \[ 120 \]