How many words (with or without meaning) of three distinct letters of the English aphabets are there?

Answer

To solve the problem of how many words (with or without meaning) can be formed using three distinct letters from the English alphabet, we can follow these steps:

### Step-by-step Solution:

1. **Identify the Total Number of Letters**:
The English alphabet consists of 26 letters.

2. **Determine the Length of the Word**:
We need to form words that are 3 letters long.

3. **Use the Permutation Formula**:
Since the letters must be distinct, we will use the permutation formula for selecting and arranging 'r' items from 'n' items, which is given by:
\[ nPr = \frac{n!}{(n-r)!} \]
Here, \( n = 26 \) (total letters) and \( r = 3 \) (letters to choose).

4. **Calculate \( 26P3 \)**:
Plugging in the values, we have:
\[ 26P3 = \frac{26!}{(26-3)!} = \frac{26!}{23!} \]
This simplifies to:
\[ 26P3 = 26 \times 25 \times 24 \]

5. **Perform the Multiplication**:
Now, calculate the product:
\[ 26 \times 25 = 650 \]
\[ 650 \times 24 = 15600 \]

6. **Final Answer**:
Therefore, the total number of distinct three-letter words that can be formed is **15600**.