A word consists of 9 letters; 5 consonants and 4 vowels. There letters are chosen at random. What is the probability that more than one vowel will be selected?
A
13/42
B
5/42
C
17/42
D
3/14
Correct Answer: 17/42
Given, Consonants = 5 Vowels = 4 Probability = = {1 - (C35C39 + C25×C14C39)} = {1 - (5!3!(5 - 3)!9!3!(9 - 3)! + 5!2!(5 - 2)!×4!1!(4 - 1)!9!3!(9 - 3)!)} = {1 - (5!3!2!9!3!6! + 5!2!3!×4!1!3!9!3!6!)} = {1 - (5×4×3!2×3!9×8×7×6!2×3×6! + 5×4×3!2×3!×4×3!3!9×8×7×6!2×3×6!)} = {1 - (1084 + 10×484)} = (1 - 5084) = (80 - 5084) = 3484 = 1742