I am given the following question:
A code consists of $4$ letters from the English alphabet and $3$ letters from the Greek alphabet. There are $8$ English letters and $6$ Greek letters to choose from and repetition is not allowed. How many $7$-letter codes are possible?
I tried solving this question by finding the number of possible combinations for the English Letters ($8C4$) and Greek Letters ($6C3$). I multiplied the two to get $1400$ different $7$ letter combinations. I multiplied $1400$ by $7!$ since there can be $7$ possible letters in the first slot, followed by $6$, and so on.
The answer that was given was $201600$ and my teacher stated that this was the case because it should be $(8P4) \times (6P3)$. Please explain what I did wrong.
Thank You :)