If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number 602 (2) 603 (3) 600 (4) 601

Options

A. 603
B. 602
C. 601
D. 600

Explanation

To solve the problem of finding the serial number of the word "SACHIN" when all its letters are arranged in alphabetical order, we can follow these steps:

### Step 1: Arrange the letters in alphabetical order
The letters of the word "SACHIN" are: S, A, C, H, I, N.
When arranged in alphabetical order, they become: A, C, H, I, N, S.

### Step 2: Calculate the total arrangements before "SACHIN"
We need to find how many words can be formed that come before "SACHIN" in the dictionary order.

1. **Fix the first letter**:
- If we fix 'A' as the first letter, the remaining letters are C, H, I, N, S. The number of arrangements of these 5 letters is:
\[ 5! = 120 \]

2. **Fix 'C' as the first letter**:
- If we fix 'C' as the first letter, the remaining letters are A, H, I, N, S. The number of arrangements is again:
\[ 5! = 120 \]

3. **Fix 'H' as the first letter**:
- If we fix 'H' as the first letter, the remaining letters are A, C, I, N, S. The number of arrangements is:
\[ 5! = 120 \]

4. **Fix 'I' as the first letter**:
- If we fix 'I' as the first letter, the remaining letters are A, C, H, N, S. The number of arrangements is:
\[ 5! = 120 \]

5. **Fix 'N' as the first letter**:
- If we fix 'N' as the first letter, the remaining letters are A, C, H, I, S. The number of arrangements is:
\[ 5! = 120 \]

### Step 3: Count the arrangements before "SACHIN"
Now, we add all the arrangements calculated above:
\[ 120 (A) + 120 (C) + 120 (H) + 120 (I) + 120 (N) = 600 \]

### Step 4: Count the arrangements that lead to "SACHIN"
Now we need to consider the arrangements that start with 'S':
- The next letters in "SACHIN" are A, C, H, I, N.
- The first letter 'S' is fixed, and we need to arrange A, C, H, I, N in that order.

### Step 5: Find the position of "SACHIN"
Since "SACHIN" is the next arrangement after all those counted before it, we add 1 to the total:
\[ 600 + 1 = 601 \]

### Conclusion
Thus, the word "SACHIN" appears at serial number **601**.

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