Question: A historian of science is studying the development of probability theory and examines a 17th-century manuscript containing all permutations of the letters in the word PROBABILITY. If the historian randomly selects one such permutation, what is the probability that the vowels appear in alphabetical order (i.e., A, I, O — but in this word, only A and I and O appear; note: PROBABILITY has letters: P, R, O, B, A, B, I, L, T, Y — vowels are A, O, I. Wait: check vowels: A, O, I. So vowels are A, I, O — and the condition is that in the permutation, A, I, O appear in alphabetical order: A before I before O. - Treasure Valley Movers