The letters of the word ' LOGARITHM' are arranged at random. The probability that arrangements starts with vowel and end with consonant is

Step-by-step solution

(C) The word LOGARITHM contains 3 vowels and 6 consonants. Starting vowel can be chosen from 3 vowels in 3 distinct ways and the end consonant could be chosen from 6 consonants in 6 distinct ways and the rest of 7 letters can be permuted among themselves in 7 ! ways. So total number of ways this arrangement could be done are 3 6 7 ! . So, the probability that words could start with vowel and end with consonant = 3 6 7 ! 9 ! = 1 4