Question related to combinations, counting and listing

Question

Assume that you are to generate computer password codes using 10 consonants and 5 vowels. How many different passwords can be generated if each password is made up of 3 consonants and 2 vowels?

Answer 1

Hint 1: The Rule of Product paraphrased says that when counting things if you can come up with a sequence of steps to uniquely describe each outcome you wish to count such that the number of options to complete each step does not depend in any way on the previously made selections, then the total number of outcomes is merely the product of the number of options per step.

Hint 2:

Pick which positions in the password are occupied by vowels. For the left-most position used by a vowel, pick which vowel it is. For the remaining position occupied by a vowel, pick which vowel it is. For the first position occupied by a consonant, pick which it is. For the next position occupied by a consonant, pick which it is. For the final position occupied by a consonant, pick which it is.