Random Letters

Suppose a word is picked at random from this sentence. Find:

1. the outcome space for this random experiment
2. the chance the word has at least 4 letters;
3. the chance that the word contains at least 2 vowels (a,e,i,o,u)
4. the chance that the word contains at least 4 letters and at least 2 vowels.
5. What is the distribution of the length of the word picked ?
6. What is the distribution of the number of vowels in the word ?

(Based on [Pitman p.9 #2 and p. 31 #6)