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. 614
B. 615
C. 613
D. 616

Answer

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

### Step 1: List the letters in alphabetical order
The letters in "RANDOM" are: A, D, M, N, O, R.
Arranging them in alphabetical order gives us: A, D, M, N, O, R.

### Step 2: Count permutations starting with letters before 'R'
We will count how many words can be formed starting with each letter that comes before 'R' (i.e., A, D, M, N, O).

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

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

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

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

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

### Step 3: Calculate total permutations before 'R'
Total permutations before 'R':
= 120 (A) + 120 (D) + 120 (M) + 120 (N) + 120 (O)
= 600

### Step 4: Count permutations starting with 'R'
Now we need to consider words starting with 'R'. We will look at the letters that come after 'R' in the alphabetical order: A, D, M, N, O.

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

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

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

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

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

### Step 5: Calculate total permutations before 'RANDOM'
Total permutations before 'RANDOM':
= 600 (from previous letters) + 24 (RA) + 24 (RD) + 24 (RM) + 24 (RN) + 24 (RO)
= 600 + 120 = 720

### Step 6: Count permutations starting with 'RAN'
Now we will consider words starting with 'RAN'. The letters that come after 'RAN' in alphabetical order are D, M, O.

1. **Starting with RAN**:
- Remaining letters: D, M, O (3 letters)
- Number of permutations = 3! = 6

### Step 7: Count permutations starting with 'RAND'
Now we will consider words starting with 'RAND'. The letters that come after 'RAND' in alphabetical order are M, O.

1. **Starting with RAND**:
- Remaining letters: M, O (2 letters)
- Number of permutations = 2! = 2

### Step 8: Count permutations starting with 'RANDO'
Finally, we will consider words starting with 'RANDO'.

1. **Starting with RANDO**:
- Remaining letters: M (1 letter)
- Number of permutations = 1! = 1

### Step 9: Calculate the position of 'RANDOM'
Now we can calculate the position of 'RANDOM':
- Total words before 'RANDOM' = 720 + 6 (for RAN) + 2 (for RAND) + 1 (for RANDO) = 729

Thus, the position of the word "RANDOM" is **730**.