1. **Problem Statement:** Find the number of permutations of $n=4$ objects taken $r=2$ at a time. 2. **Formula:** The permutation formula is given by $$P(n, r) = \frac{n!}{(n-r)!}$$ where $n!$ denotes the factorial of $n$, which is the product of all positive integers up to $n$. 3. **Substitute values:** Substitute $n=4$ and $r=2$ into the formula: $$P(4, 2) = \frac{4!}{(4-2)!} = \frac{4!}{2!}$$ 4. **Calculate factorials:** $$4! = 4 \times 3 \times 2 \times 1 = 24$$ $$2! = 2 \times 1 = 2$$ 5. **Evaluate permutation:** $$P(4, 2) = \frac{24}{2} = 12$$ 6. **Conclusion:** There are 12 different ways to arrange 4 students in 2 seats for a selfie. This means the students can be seated in 12 unique orders when only 2 seats are available.