If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in dictionary; then the position of the word SMALL is :

Question

Accepted Answer

To determine the position of the word "SMALL" when all possible five-letter words formed from the letters of "SMALL" are arranged in dictionary order, we need to consider the alphabetical order of the letters: A, L, L, M, S.

1. **Words starting with A:**
   - The remaining letters are L, L, M, S. 
   - The number of permutations of these four letters is 4! / 2! = 12 (since L is repeated twice).

2. **Words starting with L:**
   - The remaining letters are A, L, M, S.
   - The number of permutations of these four letters is 4! = 24.

3. **Words starting with M:**
   - The remaining letters are A, L, L, S.
   - The number of permutations of these four letters is 4! / 2! = 12 (since L is repeated twice).

4. **Words starting with S:**
   - The remaining letters are A, L, L, M.
   - The number of permutations of these four letters is 4! / 2! = 12 (since L is repeated twice).

Now, we need to find the position of "SMALL" among the words starting with S:

- **Words starting with SA:**
  - The remaining letters are L, L, M.
  - The number of permutations of these three letters is 3! / 2! = 3.

- **Words starting with SL:**
  - The remaining letters are A, L, M.
  - The number of permutations of these three letters is 3! = 6.

- **Words starting with SMA:**
  - The remaining letters are L, L.
  - The number of permutations of these two letters is 2! / 2! = 1.

- **Words starting with SML:**
  - The remaining letters are A, L.
  - The number of permutations of these two letters is 2! = 2.

- **Words starting with SMAL:**
  - The remaining letter is L.
  - There is only 1 permutation.

Adding these up, the position of "SMALL" is:
12 (A) + 24 (L) + 12 (M) + 3 (SA) + 6 (SL) + 1 (SMA) + 2 (SML) + 1 (SMAL) = 58.

Therefore, the position of the word "SMALL" is 58th, which confirms that Option 4 is the correct answer.

**Explanation of Incorrect Options:**

- **Option 1 (46th):** This position is too early in the sequence, as it does not account for the correct number of permutations before reaching words starting with "SMALL."
  
- **Option 2 (59th):** This position is one step beyond the correct position, as it would imply an additional permutation that does not exist.

- **Option 3 (52nd):** This position is also too early, similar to Option 1, and does not account for all permutations leading up to "SMALL."

Thus, Option 4 is the only correct answer, as it accurately reflects the position of "SMALL" in the dictionary order of permutations.