Question

The word geometry has eight letters. Three letters are chosen at random.

What is the probability that two consonants and one vowel are chosen?

0.536
0.268
0.179
0.089

Answer 1

Letters (by position) in "geometry": vowels = e, o, e (3); consonants = g, m, t, r, y (5). Number of ways to choose 2 consonants and 1 vowel = C(5,2)·C(3,1) = 10·3 = 30. Total ways = C(8,3) = 56. Probability = 30/56 = 15/28 ≈ 0.536.

Answer: 0.536.