The eight letter-tiles of the word EQUATION are put in a bag and three tiles are taken out together at random. What is the probability that all three tiles carry vowels?

EQUATION has 8 different letters, of which E, U, A, I, O are vowels and Q, T, N are consonants. Total draws = C(8,3) = 56, and all-vowel draws = C(5,3) = 10, so the probability is 10/56 = 5/28. Trap 15/28 = 30/56 is 'exactly two vowels', C(5,2) × C(3,1). Trap 1/56 is the all-consonant draw. Trap 5/8 is the chance for a SINGLE tile and ignores that the bag shrinks as tiles come out.