How many 4 letter code can be formed using the first 10 letters of the english alphabet if no letter can be repeated.

Options

A. 35
B. 30
C. 50
D. 60

Explanation

To solve the problem of how many 4-letter codes can be formed using the first 10 letters of the English alphabet without repeating any letters, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the total number of available letters**:
We have the first 10 letters of the English alphabet, which are A, B, C, D, E, F, G, H, I, and J. Therefore, the total number of available letters is 10.

2. **Determine the choices for each letter in the code**:
- For the **first letter**, we can choose any of the 10 letters.
- For the **second letter**, since we cannot repeat the first letter, we have 9 remaining choices.
- For the **third letter**, we cannot use the first two letters, leaving us with 8 choices.
- For the **fourth letter**, we cannot use the first three letters, which gives us 7 choices.

3. **Calculate the total number of combinations**:
The total number of ways to form the 4-letter code can be calculated by multiplying the number of choices for each letter:
\[ \text{Total combinations} = 10 \times 9 \times 8 \times 7 \]

4. **Perform the multiplication**:
- First, calculate \(10 \times 9 = 90\)
- Next, calculate \(90 \times 8 = 720\)
- Finally, calculate \(720 \times 7 = 5040\)

5. **Conclusion**:
Thus, the total number of 4-letter codes that can be formed using the first 10 letters of the English alphabet without repeating any letters is **5040**.