A dictionary compriing of four lettered words is formed by arranging individually the letters of the words SLOW and FAST. What is rank of the word SLOW?

Answer

To find the rank of the word "SLOW" in a dictionary formed by the arrangements of the letters of the words "SLOW" and "FAST", we will follow these steps:

### Step 1: List the Letters
The letters in "SLOW" are S, L, O, and W.

### Step 2: Arrange the Letters in Alphabetical Order
We need to arrange the letters in alphabetical order:
- The alphabetical order of the letters is: **L, O, S, W**.

### Step 3: Count Words Before "SLOW"
To find the rank of "SLOW", we need to count how many words would come before it in a dictionary.

1. **Words starting with L**:
- Remaining letters: O, S, W
- The number of arrangements = 3! = 6

2. **Words starting with O**:
- Remaining letters: L, S, W
- The number of arrangements = 3! = 6

3. **Words starting with S**:
- Now we fix S and look at the next letter.
- Remaining letters: L, O, W

### Step 4: Count Words Starting with SL
1. **Words starting with SL**:
- Remaining letters: O, W
- The number of arrangements = 2! = 2

### Step 5: Count Words Starting with SO
1. **Words starting with SO**:
- Remaining letters: L, W
- The number of arrangements = 2! = 2

### Step 6: Count Words Starting with SW
1. **Words starting with SW**:
- Remaining letters: L, O
- The number of arrangements = 2! = 2

### Step 7: Total Count of Words Before "SLOW"
Now, we sum all the counts:
- Words starting with L: 6
- Words starting with O: 6
- Words starting with SL: 2
- Words starting with SO: 2
- Words starting with SW: 0 (since SLOW is the next arrangement)

Total words before "SLOW" = 6 + 6 + 2 + 2 = 16

### Step 8: Calculate the Rank
The rank of "SLOW" is the total number of words before it plus 1 (to include "SLOW" itself):
- Rank of "SLOW" = 16 + 1 = 17

### Final Answer
The rank of the word "SLOW" is **17**.

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