A word consists of 9 letters; 5 consonants and 4 vowels.Three letters are choosen at random. What is the probability that more than one vowel will be selected ?

3 letters can be choosen out of 9 letters in $9C3$ ways.

More than one vowels ( 2 vowels + 1 consonant  or  3 vowels ) can be choosen in  $(4C2*5C1)+4C3$ ways

Hence,required probability = $\frac{4C2*5C1+4C3}{9C3}$ = 17/42