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. (a) 603
B. (b) 602
C. (c) 601
D. (d) 600

Explanation

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

### Step 1: List the letters in alphabetical order
The letters in "SACHIN" are: A, C, H, I, N, S.
In alphabetical order, they are: A, C, H, I, N, S.

### Step 2: Count the arrangements starting with letters before 'S'
1. **Starting with 'A':**
- Remaining letters: C, H, I, N, S
- Number of arrangements = 5! = 120

2. **Starting with 'C':**
- Remaining letters: A, H, I, N, S
- Number of arrangements = 5! = 120

3. **Starting with 'H':**
- Remaining letters: A, C, I, N, S
- Number of arrangements = 5! = 120

4. **Starting with 'I':**
- Remaining letters: A, C, H, N, S
- Number of arrangements = 5! = 120

5. **Starting with 'N':**
- Remaining letters: A, C, H, I, S
- Number of arrangements = 5! = 120

### Step 3: Count the arrangements starting with 'S'
Now we consider the arrangements starting with 'S':
- The next letters in alphabetical order after 'S' are A, C, H, I, N.

1. **Starting with 'SA':**
- Remaining letters: C, H, I, N
- Number of arrangements = 4! = 24

2. **Starting with 'SC':**
- Remaining letters: A, H, I, N
- Number of arrangements = 4! = 24

3. **Starting with 'SH':**
- Remaining letters: A, C, I, N
- Number of arrangements = 4! = 24

4. **Starting with 'SI':**
- Remaining letters: A, C, H, N
- Number of arrangements = 4! = 24

5. **Starting with 'SN':**
- Remaining letters: A, C, H, I
- Number of arrangements = 4! = 24

### Step 4: Count the arrangements leading up to 'SACHIN'
Now we will count the arrangements that lead up to the word "SACHIN":
- Up to 'S': 120 + 120 + 120 + 120 + 120 = 600
- Up to 'SA': 24
- Up to 'SAC': 6 (since the remaining letters are H, I, N)
- Up to 'SACH': 2 (since the remaining letters are I, N)
- Finally, we have "SACHIN" itself.

### Step 5: Calculate the total
Adding these up:
- Total = 600 (for letters before 'S') + 24 (for 'SA') + 6 (for 'SAC') + 2 (for 'SACH') + 1 (for 'SACHIN') = 633.

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

### Final Answer
The word "SACHIN" appears at serial number **601**.

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