If all the words formed with the letters of the word 'RANDOM' arranged in a dictionary then the word 'RANDOM' will be placed at position no:

Options

A. 610
B. 612
C. 614
D. None of these

Answer

To find the position of the word "RANDOM" when all the permutations of its letters are arranged in alphabetical order, we can follow these steps:

### Step 1: List the letters of the word
The letters in "RANDOM" are: A, D, M, N, O, R.

### Step 2: Arrange the letters in alphabetical order
The alphabetical order of the letters is: A, D, M, N, O, R.

### Step 3: Count permutations starting with letters before 'R'
1. **Words starting with 'A':**
- Remaining letters: D, M, N, O, R (5 letters)
- Number of permutations = 5! = 120

2. **Words starting with 'D':**
- Remaining letters: A, M, N, O, R (5 letters)
- Number of permutations = 5! = 120

3. **Words starting with 'M':**
- Remaining letters: A, D, N, O, R (5 letters)
- Number of permutations = 5! = 120

4. **Words starting with 'N':**
- Remaining letters: A, D, M, O, R (5 letters)
- Number of permutations = 5! = 120

5. **Words starting with 'O':**
- Remaining letters: A, D, M, N, R (5 letters)
- Number of permutations = 5! = 120

### Step 4: Count permutations starting with 'R'
Now we need to consider the words starting with 'R'. The next letter in "RANDOM" is 'A'.

1. **Words starting with 'RA':**
- Remaining letters: D, M, N, O (4 letters)
- Number of permutations = 4! = 24

2. **Words starting with 'RD':**
- Remaining letters: A, M, N, O (4 letters)
- Number of permutations = 4! = 24

3. **Words starting with 'RM':**
- Remaining letters: A, D, N, O (4 letters)
- Number of permutations = 4! = 24

4. **Words starting with 'RN':**
- Remaining letters: A, D, M, O (4 letters)
- Number of permutations = 4! = 24

5. **Words starting with 'RO':**
- Remaining letters: A, D, M, N (4 letters)
- Number of permutations = 4! = 24

### Step 5: Count permutations starting with 'RAN'
Next, we consider the letters starting with 'RAN'.

1. **Words starting with 'RAN':**
- The next letter in "RANDOM" is 'D'.
- Remaining letters: O, M (2 letters)
- Number of permutations = 2! = 2 (i.e., "RANOM" and "RANOD")

### Step 6: Count the total permutations before "RANDOM"
Now, we can sum up all the permutations calculated:
- Words starting with 'A': 120
- Words starting with 'D': 120
- Words starting with 'M': 120
- Words starting with 'N': 120
- Words starting with 'O': 120
- Words starting with 'RA': 24
- Words starting with 'RD': 24
- Words starting with 'RM': 24
- Words starting with 'RN': 24
- Words starting with 'RO': 24
- Words starting with 'RAN': 2 (before "RANDOM")

Total = 120 + 120 + 120 + 120 + 120 + 24 + 24 + 24 + 24 + 24 + 2 = 624

### Step 7: Determine the position of "RANDOM"
Since "RANDOM" is the next word after all those counted, its position is:
624 + 1 = 625.

Thus, the position of the word "RANDOM" in the dictionary is **625**.