State True or False : Total number of two letter word, when repetition of letter is not allowed is `P(26,2)`

Answer

To determine whether the statement "Total number of two-letter words, when repetition of letters is not allowed, is \( P(26, 2) \)" is true or false, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: We need to find the total number of two-letter words that can be formed using the English alphabet (which has 26 letters) without allowing any letter to repeat.

2. **Choosing the First Letter**: For the first letter of the two-letter word, we can choose any of the 26 letters from the alphabet.

3. **Choosing the Second Letter**: Since repetition is not allowed, once we have chosen the first letter, we have 25 letters left to choose from for the second letter.

4. **Calculating the Total Combinations**: The total number of ways to form a two-letter word can be calculated as:
\[ \text{Total combinations} = \text{Choices for first letter} \times \text{Choices for second letter} = 26 \times 25 \]

5. **Using Permutations**: The number of ways to arrange \( r \) items from \( n \) items without repetition is given by the permutation formula \( P(n, r) = \frac{n!}{(n-r)!} \). In this case, we have:
\[ P(26, 2) = \frac{26!}{(26-2)!} = \frac{26!}{24!} = 26 \times 25 \]

6. **Conclusion**: Since the total number of two-letter words without repetition is indeed \( 26 \times 25 \), we can conclude that the statement is true. Therefore, the statement "Total number of two-letter words, when repetition of letters is not allowed, is \( P(26, 2) \)" is **True**.

### Final Answer:
**True**