a)First letter a consonant, did I read well?
Suppose you put the H in the first place; you get
H _ _ _ _ _ that means you have 5 letters to put in 5 places; thatīs a permutation of 5 elements:
Doing the same with the other consonants it means that you have ways.
b) _ vowel _ _ vowel _
and you only have two possibilities:
_ A _ _ E _ (permutation of 4 elements)
_ E _ _ A _ (permutation of 4 elements)
that leads to
Iīm assuming there are no repeated letters on an arrangement.