All word , with or without meaning ,are made using all the letters of the word MONDAY . These words are written as in a dictionary with serial numbers .The serial number of the word MONDAY is

Options

A. `327`
B. `326`
C. `328`
D. `324`

Answer

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

### Step-by-Step Solution:

1. **Identify the Letters**: The letters in "MONDAY" are M, O, N, D, A, Y.

2. **Arrange the Letters in Alphabetical Order**: The alphabetical order of the letters is A, D, M, N, O, Y.

3. **Count Words Starting with Each Letter Before 'M'**:
- **Words starting with 'A'**: The remaining letters are D, M, N, O, Y. The number of permutations is \(5! = 120\).
- **Words starting with 'D'**: The remaining letters are A, M, N, O, Y. The number of permutations is \(5! = 120\).

Total words starting with A or D = \(120 + 120 = 240\).

4. **Count Words Starting with 'M'**:
- Next, we consider words starting with 'M'. The remaining letters are A, D, N, O, Y. We will count the words starting with each of these letters.

5. **Words Starting with 'MA'**: The remaining letters are D, N, O, Y. The number of permutations is \(4! = 24\).

6. **Words Starting with 'MD'**: The remaining letters are A, N, O, Y. The number of permutations is \(4! = 24\).

7. **Words Starting with 'MN'**: The remaining letters are A, D, O, Y. The number of permutations is \(4! = 24\).

8. **Words Starting with 'MO'**:
- **Words Starting with 'MOA'**: The remaining letters are D, N, Y. The number of permutations is \(3! = 6\).
- **Words Starting with 'MOD'**: The remaining letters are A, N, Y. The number of permutations is \(3! = 6\).
- **Words Starting with 'MON'**:
- **Words Starting with 'MONA'**: The remaining letters are D, Y. The number of permutations is \(2! = 2\).
- **Words Starting with 'MOND'**: The remaining letters are A, Y. The number of permutations is \(2! = 2\).
- **Finally, 'MONDAY'**: This is the word we are looking for, which counts as 1.

9. **Calculate the Total**:
- Total words before "MONDAY" =
- Words starting with A and D: \(240\)
- Words starting with MA: \(24\)
- Words starting with MD: \(24\)
- Words starting with MN: \(24\)
- Words starting with MOA: \(6\)
- Words starting with MOD: \(6\)
- Words starting with MONA: \(2\)
- Words starting with MOND: \(2\)
- Finally, add 1 for "MONDAY".

Total = \(240 + 24 + 24 + 24 + 6 + 6 + 2 + 2 + 1 = 329\).

### Final Answer:
The serial number of the word "MONDAY" is **330**.