# what is the probability given some constraints

This is an exercise question on probability: If each coded item in a catalog begins with 2 distinct letters followed by 3 distinct nonzero digits, find the probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even.
Here's how I attempted it.
The sample space is: 26*25*9*8*7 (unique letters and non zero digits)

The numerator is: 5(number of possible vowels)* 25(can be anything)* 4 (possible even digits other than zero) * 8 (rest of the digits)*7(rest of the digits). Is this approach ok?

Probability = $\frac{5 × 25 × 7 × 8 × 4}{26 × 25 × 9 × 8 × 7}$