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 3 ligands of type 'a', 2 ligands of type 'b', and 1 ligand of type 'c'.
2. **Possible Isomers**:
- The arrangement of the 'a' ligands can be either in a cis or trans configuration relative to the other ligands.
- The 'b' and 'c' ligands can also be arranged in different orientations.
3. **Count the Isomers**:
- For the arrangement of 'a' ligands, we can have configurations like:
- All 'a' ligands together (cis).
- One 'a' ligand opposite to the others (trans).
- This results in 3 distinct arrangements for the 'a' ligands.
4. **Total Isomers**: After considering the arrangements of 'b' and 'c', we find that there are **3 space isomers** for this compound.

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

1. **Identify the Ligands**: Here, 'AB' is a bidentate ligand, meaning it can bind to the metal at two sites.
2. **Possible Isomers**:
- Since there are three bidentate ligands, the arrangement can lead to different spatial orientations.
- The ligands can be arranged in a way that some are cis and some are trans.
3. **Count the Isomers**:
- Each bidentate ligand can create two different orientations (cis and trans).
- This leads to a total of **4 space isomers** (considering optical activity as well).

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

1. **Identify the Ligands**: This compound has 2 ligands of type 'a', 2 ligands of type 'b', and 2 ligands of type 'c'.
2. **Possible Isomers**:
- The arrangement of 'a', 'b', and 'c' ligands can lead to various spatial configurations.
- The ligands can be arranged in cis and trans forms.
3. **Count the Isomers**:
- For this compound, we can have multiple configurations leading to a total of **6 space isomers**.

### Final Summary of Isomers:
- For Compound I: 3 space isomers
- For Compound II: 4 space isomers
- For Compound III: 6 space isomers

### Conclusion:
The correct code regarding the total number of space isomers for the compounds is **3, 4, 6**.

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