1. **Problem statement:** We have 10 athletes standing in a row for a photo, and the tallest athlete must be positioned exactly in the center. 2. **Understanding the problem:** Since there are 10 athletes, the center position is the 5th position (if counting from 1 to 10, the middle is between 5 and 6, but since the tallest must be exactly centered, we consider the 5th position as the center for this problem). 3. **Key rule:** The tallest athlete is fixed in the center position, so we do not permute this athlete. 4. **Permuting the remaining athletes:** There are 9 other athletes to arrange in the remaining 9 positions. 5. **Formula for permutations:** The number of ways to arrange $n$ distinct objects is $n!$. 6. **Applying the formula:** The number of different photos possible is the number of ways to arrange the 9 remaining athletes, which is $$9! = 362880.$$ **Final answer:** There are $362880$ different photos possible with the tallest athlete centered.