1. The problem asks to evaluate the permutation expression $6P5$. 2. The formula for permutations is: $$nP r = \frac{n!}{(n-r)!}$$ where $n$ is the total number of items, and $r$ is the number of items to arrange. 3. Substitute $n=6$ and $r=5$ into the formula: $$6P5 = \frac{6!}{(6-5)!} = \frac{6!}{1!}$$ 4. Calculate factorials: $$6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720$$ $$1! = 1$$ 5. Simplify the fraction: $$6P5 = \frac{720}{1} = 720$$ 6. Since the result is an integer, the answer is: $$6P5 = 720$$ This means there are 720 ways to arrange 5 items out of 6 in order.