1. **Problem statement:** Amy and her 4 close friends stand in a line with Amy exactly in the middle. We need to find how many different ways they can stand in such a line. 2. **Understanding the problem:** There are 5 people total: Amy + 4 friends. 3. **Key point:** Amy must be in the middle position of the line. Since there are 5 people, the middle position is the 3rd position. 4. **Step-by-step solution:** - Fix Amy in the 3rd position. - Arrange the 4 friends in the remaining 4 positions (1st, 2nd, 4th, 5th). 5. **Formula used:** The number of ways to arrange $n$ distinct people in $n$ positions is $n!$ (factorial). 6. **Calculate:** Number of ways to arrange 4 friends in 4 positions is $4! = 4 \times 3 \times 2 \times 1 = 24$. 7. **Final answer:** There are $24$ different ways for them to stand in a line with Amy in the middle.