How many pairs of enantiomers are possible for `[M(A A)(BC)de]` ? .

Explanation

To determine how many pairs of enantiomers are possible for the coordination compound `[M(A A)(BC)de]`, we will follow these steps:

### Step 1: Understand the Structure
The coordination compound consists of a metal center (M) surrounded by ligands. In this case, we have:
- A bidentate ligand (AA)
- Two bidentate ligands (BC)
- Two monodentate ligands (d and e)

### Step 2: Identify the Coordination Number
The coordination number of the metal (M) is 6, as it is coordinated by two bidentate ligands and two monodentate ligands.

### Step 3: Determine the Types of Isomers
For coordination compounds, we can have:
- Geometric isomers (cis/trans)
- Optical isomers (enantiomers)

Since we are interested in enantiomers, we need to focus on the optical activity of the structures.

### Step 4: Draw Possible Structures
1. **First Structure**: Place AA in one position and BC in the other positions. This gives us an optically active structure.
2. **Second Structure**: Swap the positions of B and C while keeping AA in the same position. This is another optically active structure.
3. **Third Structure**: Change the orientation of the bidentate ligands while keeping the positions of d and e constant. This gives us a new structure.
4. **Fourth Structure**: Similar to the third, but swap the positions of d and e.

Continue this process until you have exhausted all unique arrangements of the ligands that result in optically active structures.

### Step 5: Count the Unique Optical Isomers
After drawing the structures, we find that there are 10 unique optical isomers. Since each optical isomer has a non-superimposable mirror image, we can pair them up.

### Step 6: Calculate Pairs of Enantiomers
Since we have 10 optical isomers, we can form 5 pairs of enantiomers (each pair consisting of an isomer and its mirror image).

### Final Answer
Thus, the total number of pairs of enantiomers possible for the coordination compound `[M(A A)(BC)de]` is **5**.

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