Calculate the number of Benzenoid isomers possible for `C_(6)H_(3)ClBrl`.

Explanation

To calculate the number of benzenoid isomers for the molecular formula \( C_6H_3ClBrI \), we can follow these steps:

### Step 1: Understand the Structure
Benzene has a hexagonal ring structure with alternating double bonds. For the formula \( C_6H_3ClBrI \), we have a benzene ring where three hydrogen atoms are replaced by one chlorine (Cl), one bromine (Br), and one iodine (I) atom.

### Step 2: Identify Positions for Substituents
The positions on the benzene ring are typically numbered as follows:
1. Position 1 (C1)
2. Position 2 (C2)
3. Position 3 (C3)
4. Position 4 (C4)
5. Position 5 (C5)
6. Position 6 (C6)

### Step 3: Consider Different Arrangements
We need to consider the different arrangements of Cl, Br, and I on the benzene ring. Since the substituents are different, we can use the concept of fixing one substituent and arranging the others around it.

### Step 4: Fix One Substituent
1. **Fix Cl at Position 1**:
- Possible arrangements for Br and I:
- Br at Position 2, I at Position 3
- Br at Position 3, I at Position 2
- Br at Position 4, I at Position 5
- Br at Position 5, I at Position 4
- Br at Position 6, I at Position 5
- Br at Position 5, I at Position 6

2. **Fix Br at Position 1**:
- Possible arrangements for Cl and I:
- Cl at Position 2, I at Position 3
- Cl at Position 3, I at Position 2
- Cl at Position 4, I at Position 5
- Cl at Position 5, I at Position 4
- Cl at Position 6, I at Position 5
- Cl at Position 5, I at Position 6

3. **Fix I at Position 1**:
- Possible arrangements for Cl and Br:
- Cl at Position 2, Br at Position 3
- Cl at Position 3, Br at Position 2
- Cl at Position 4, Br at Position 5
- Cl at Position 5, Br at Position 4
- Cl at Position 6, Br at Position 5
- Cl at Position 5, Br at Position 6

### Step 5: Count the Isomers
After considering all the arrangements by fixing each substituent in turn, we find that there are a total of **10 distinct benzenoid isomers** for \( C_6H_3ClBrI \).

### Final Answer
The total number of benzenoid isomers for \( C_6H_3ClBrI \) is **10**.

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