All possible 120 permutations of WDSMC are arranged in dictionary order, as if each were an ordinary five- letter word. The last letter of the ` 86^(th)` word in the list, is :
i) W
ii) D
iii) M
iv) C

Options

A. W
B. D
C. M
D. C

Answer

To solve the problem of finding the last letter of the 86th permutation of the letters W, D, S, M, and C arranged in dictionary order, we can follow these steps:

### Step-by-Step Solution:

1. **Arrange the letters in alphabetical order**:
The letters W, D, S, M, and C in alphabetical order are:
C, D, M, S, W.

2. **Count permutations starting with each letter**:
- **Words starting with C**:
The remaining letters are D, M, S, W. The number of permutations of these 4 letters is \(4! = 24\).
- **Words starting with D**:
The remaining letters are C, M, S, W. The number of permutations is also \(4! = 24\).
- **Total words starting with C and D**:
\(24 + 24 = 48\).

3. **Continue counting with the next letter**:
- **Words starting with M**:
The remaining letters are C, D, S, W. The number of permutations is \(4! = 24\).
- **Total words starting with C, D, and M**:
\(48 + 24 = 72\).

4. **Next letter is S**:
- **Words starting with S**:
The remaining letters are C, D, M, W. We need to consider the permutations starting with S.
- **Words starting with S and C**:
The remaining letters are D, M, W. The number of permutations is \(3! = 6\).
- **Total words starting with C and D**:
\(72 + 6 = 78\).

5. **Continue with S and D**:
- **Words starting with S and D**:
The remaining letters are C, M, W. The number of permutations is \(3! = 6\).
- **Total words starting with S, C, and D**:
\(78 + 6 = 84\).

6. **Next, consider S and M**:
- **Words starting with S and M**:
The remaining letters are C, D, W. The number of permutations is \(3! = 6\).
- **Total words starting with S, C, D, and M**:
\(84 + 6 = 90\).

7. **Find the 86th word**:
Since we have reached 90 with S and M, we need to find the specific arrangement for the 86th word.
- The 85th word will start with S, followed by C, D, W.
- The 86th word will be S, followed by M, and then the remaining letters C and D.

8. **Determine the last letter of the 86th word**:
The 86th word is S, M, C, D, W. The last letter is W.

### Conclusion:
The last letter of the 86th word in the list is **W**.