The letters of the word ' LOGARITHM' are arranged at random. The probability that arrangements starts with…
The letters of the word ' LOGARITHM' are arranged at random. The probability that arrangements starts with vowel and end with consonant is
$\frac{71}{9 !}$
$\frac{18}{9 !}$
$\frac{1}{4}$
$\frac{1}{9}$
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 $3 \times 6 \times 7 !$.
So, the probability that words could start with vowel and end with consonant $=\frac{3 \times 6 \times 7 !}{9 !}=\frac{1}{4}$