Question: Evaluate the expression. If the answer is not an integer, round to four decimal places. 6P5 …

Evaluate the expression. If the answer is not an integer, round to four decimal places. 6P5 … Select the correct factorial formula below and, if necessary, fill in the answer boxes to complete your choice. A. The factorial formula for nPk = n! / k!(n - k)!, therefore 6P5 = 6! / (6 - 5)! B. The factorial formula for nPk = n! / k!, therefore 6P5 = 6! / 5! C. The factorial formula for nPk = n! / (n - k)!, therefore 6P5 = 6! / (6 - 5)!

Solution

The problem requires evaluating the permutation \( ^6P_5 \) using the appropriate factorial formula. The permutation formula is given by: \[ ^nP_k = \frac{n!}{(n-k)!} \] This formula corresponds to option C in the choices provided. Let’s calculate \( ^6P_5 \): \[ \begin{align*} ^6P_5 &= \frac{6!}{(6-5)!} \\ &= \frac{6!}{1!} \\ &= 6 \times 5 \times 4 \times 3 \times 2 \times 1 \\ &= 720 \end{align*} \] Therefore, the value of \( ^6P_5 \) is 720.