If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is : (1) 46th (2) 59th (3) 52nd (4) 58th

Options

A. 59th
B. 52nd
C. 58th
D. 64th

Explanation

To find the position of the word "SMALL" when all possible five-letter words formed from the letters of "SMALL" are arranged in alphabetical order, we will follow these steps:

### Step 1: Arrange the letters in alphabetical order
The letters in "SMALL" are A, L, L, M, S. Arranging them in alphabetical order gives us: A, L, L, M, S.

### Step 2: Count words starting with each letter before 'S'
1. **Words starting with 'A':**
- Remaining letters: L, L, M, S
- The number of arrangements = \( \frac{4!}{2!} = \frac{24}{2} = 12 \) (since L is repeated)

2. **Words starting with 'L':**
- Remaining letters: A, L, M, S
- The number of arrangements = \( 4! = 24 \) (no letters are repeated)

3. **Words starting with 'M':**
- Remaining letters: A, L, L, S
- The number of arrangements = \( \frac{4!}{2!} = \frac{24}{2} = 12 \) (since L is repeated)

### Step 3: Count words starting with 'S'
Now, we need to consider words starting with 'S' since "SMALL" starts with 'S'.

1. **Words starting with 'S' and 'A':**
- Remaining letters: L, L, M
- The number of arrangements = \( \frac{3!}{2!} = \frac{6}{2} = 3 \) (since L is repeated)

2. **Words starting with 'S' and 'L':**
- Remaining letters: A, L, M
- The number of arrangements = \( 3! = 6 \) (no letters are repeated)

3. **Words starting with 'S' and 'M':**
- Remaining letters: A, L, L
- The next letter after 'S' is 'M', so we need to consider words starting with 'S' and 'M':
- Remaining letters: A, L, L
- The number of arrangements = \( \frac{3!}{2!} = \frac{6}{2} = 3 \) (since L is repeated)

### Step 4: Count the total number of words before "SMALL"
Now, we can sum up all the arrangements before "SMALL":
- Words starting with 'A': 12
- Words starting with 'L': 24
- Words starting with 'M': 12
- Words starting with 'S' and 'A': 3
- Words starting with 'S' and 'L': 6

Total = \( 12 + 24 + 12 + 3 + 6 = 57 \)

### Step 5: Find the position of "SMALL"
Since "SMALL" is the next word after all the counted words, we add 1 to the total:
- Position of "SMALL" = 57 + 1 = 58

Thus, the position of the word "SMALL" in the dictionary is **58th**.

### Final Answer:
(4) 58th

---