Suppose I have a vehicle registration plate model that uses $3$ letters and $5$ numbers. There cannot be no repetitions in the plate.
Suppose the second letter is Z and the last number is $0$. How many combinations can I have?
- For letters: (assuming $26$ letters) I have $\underbrace{25}_{26 - 1} \times \underbrace{1}_{\text{Z}} \times \underbrace{24}_{26 - 1 - 1}$.
For numbers, same thought: $9 \times 8 \times 7 \times 6 \times 1$.
The answer would be the multiplication of these results. Is this the correct way?
Yes, that is the correct way. The result is just the product of the different possibilities for each slot.