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Let's break down this problem step-by-step:

We are tasked with assigning 5 lockers (out of 7) to 3 male students and 2 female students, under the constraint that no male and female lockers are adjacent to each other.

The layout of the lockers, as per the figure, is a 3x3 grid with the middle square missing, so the 7 lockers are:

```
1 2
3 4
5 6 7
```

Here, the condition is that the female students’ lockers must not be adjacent to the male students' lockers.

### Step-by-step solution:

1. **Case Division: Female Lockers Placement**  
   Since the question suggests dividing the cases based on the female students’ lockers, let’s consider how to place the female students first.
   - The positions of the female students can be selected in such a way that no male locker is adjacent to a female locker.
   - There are a total of 7 lockers, and we need to place 2 female students. Once the female students are placed, the remaining 3 lockers will automatically be assigned to male students.

2. **Restrictions and Choices:**
   - The female lockers need to be non-adjacent, so we need to find combinations of 2 lockers that are not adjacent in the grid.

3. **Locker adjacency:**  
   Looking at the grid, the following pairs of lockers are adjacent:
   - 1 and 2
   - 1 and 3
   - 2 and 4
   - 3 and 5
   - 4 and 6
   - 5 and 6
   - 6 and 7

   We need to find combinations of 2 lockers that are not adjacent from this set.

4. **Selecting Female Lockers (non-adjacent pairs):**
   The following combinations of two lockers are not adjacent:
   - (1, 4)
   - (1, 6)
   - (2, 5)
   - (2, 7)
   - (3, 6)
   - (4, 7)

   So, there are 6 possible ways to assign lockers to the 2 female students.

5. **Assigning Male Lockers:**
   After placing the female students in any of the 6 valid pairs of lockers, the remaining 3 lockers will be assigned to the male students. For each combination of female students, the 3 male students can be arranged in the remaining lockers in \(3! = 6\) ways.

### Final Calculation:
- There are 6 ways to choose valid, non-adjacent lockers for the female students.
- For each of these 6 ways, there are 6 different ways to assign lockers to the male students.

Therefore, the total number of ways to assign the lockers is:
\[
6 \times 6 = 36
\]

Thus, the total number of possible cases is **36**.

---

Would you like a deeper explanation of any part of the solution or more details on the constraints? Let me know!

Here are 5 related questions to consider:
1. What would happen if there were 4 male students and 1 female student instead?
2. How would the solution change if the adjacency constraint only applied to vertically adjacent lockers?
3. What if we had to assign lockers to 2 male students and 3 female students, with the same adjacency rule?
4. How would adding a second constraint (e.g., a student cannot be assigned to a specific locker) affect the total?
5. Can you generalize this problem to larger grids of lockers, with similar adjacency restrictions?

**Tip:** When working with constraints and combinations, always try to simplify the problem by isolating one variable or condition first. In this case, focusing on the female students first made the problem more manageable.

Out of 7 lockers, 5 lockers are to be assigned to 3 male students and 2 female students, with each student receiving one locker. On the same floor, male and female students' lockers should not be adjacent to each other. Find the total number of possible cases.

Solve a combinatorics problem where 5 lockers are assigned to 3 male students and 2 female students, ensuring that no male and female lockers are adjacent. This detailed step-by-step solution includes selecting non-adjacent lockers and using combinations and factorials.

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