Select the correct code regarding total number of space isomers for the following compounds:
(I) `[Ma_(3)b_(2)c]^(n+-)`
(II) `[M(AB)_(3)]^(n+-)`
(III) `[Ma_(2)b_(2)c_(2)]^(n+-)`

Options

A. (I)-4,(II)-4,(III)-6
B. (I)-4,(II)-3,(III)-5
C. (I)-3,(II)-3,(III)-5
D. (I)-3,(II)-4,(III)-6

Explanation

To determine the total number of space isomers for the given coordination compounds, we will analyze each compound step by step.

### Step 1: Analyze Compound I - `[Ma_(3)b_(2)c]^(n+-)`

1. **Identify the Ligands**: The compound has three 'A' ligands, two 'B' ligands, and one 'C' ligand.
2. **Cis and Trans Isomers**:
- **Cis Isomer**: The 'A' ligands can be positioned adjacent to each other. This gives us one distinct cis configuration.
- **Trans Isomers**: The 'A' ligands can also be positioned opposite to each other. We can have two distinct trans configurations:
- One with 'A' ligands on one side and 'B' ligands on the other.
- Another with 'A' ligands on opposite sides.
3. **Total Isomers**:
- 1 (cis) + 2 (trans) = 3 total isomers.
4. **Optical Activity**: All isomers are optically inactive.

### Step 2: Analyze Compound II - `[M(AB)_(3)]^(n+-)`

1. **Identify the Ligands**: The compound has three bidentate ligands 'AB'.
2. **Cis and Trans Isomers**:
- **Cis Isomers**: There is one distinct configuration where the 'AB' ligands are adjacent.
- **Trans Isomers**: There are two distinct configurations where the 'AB' ligands are opposite each other.
3. **Total Isomers**:
- 1 (cis) + 2 (trans) = 3 total isomers.
4. **Optical Activity**: Both configurations are optically active.

### Step 3: Analyze Compound III - `[Ma_(2)b_(2)c_(2)]^(n+-)`

1. **Identify the Ligands**: The compound has two 'A' ligands, two 'B' ligands, and two 'C' ligands.
2. **Cis and Trans Isomers**:
- **Cis Isomers**: There is one distinct configuration where two 'A' ligands are adjacent, and the same for 'B' and 'C'.
- **Trans Isomers**: There are four distinct configurations where 'A', 'B', and 'C' ligands are positioned opposite each other.
3. **Total Isomers**:
- 1 (cis) + 4 (trans) = 5 total isomers.
4. **Optical Activity**: The cis isomer is optically active, while the trans isomers are optically inactive.

### Summary of Total Space Isomers
- **Compound I**: 3 isomers
- **Compound II**: 4 isomers
- **Compound III**: 6 isomers

### Final Answer
The correct code regarding the total number of space isomers is:
- Compound I: 3
- Compound II: 4
- Compound III: 6

Thus, the answer is **3, 4, 6**.