1. **State the problem:** Evaluate the permutation expression $7P2$. 2. **Recall the formula for permutations:** $$nP r = \frac{n!}{(n-r)!}$$ where $n$ is the total number of items, and $r$ is the number of items to arrange. 3. **Apply the formula:** $$7P2 = \frac{7!}{(7-2)!} = \frac{7!}{5!}$$ 4. **Calculate factorials:** $$7! = 7 \times 6 \times 5!$$ So, $$\frac{7!}{5!} = \frac{7 \times 6 \times 5!}{5!}$$ 5. **Cancel common factors:** $$= 7 \times 6 = 42$$ 6. **Interpret the result:** The value is an integer. **Final answer:** $$7P2 = 42$$