5. (25 points) As usual, the English alphabet consists of 26 letters: 5 vowels and 21 con- sonants. In each problem below, repetition is allowed. (a) How many 5 letter words are possible? (b) How many 5 letter words contain at least one vowel? (c) How many 5 letter words contain exactly one vowel? (d) How many 5 letter words contain exactly three vowels? (e) How many 5 letter words contain at least one a and at least one e? Hint: Use Inclusion-Exclusion to count the complement.