Find the probability that in a random arrangement of the letters of the word 'SOCIAL' vowels come together.
there are 3 vowels and 3 other letters.as the 3 vowels are to be together, consider them as one objet. therefore there are 4 objects totally, which can be arranged in 4! ways, but, the vowels can be arranged intertnally in 3! ways.
therefore total no. of ways of arranging the word with the vowels together is 4! x 3!= 24*6 = 144.
that is, no.of words with vowels together is 144.
now, total no. of ways of arranging the word is 6! = 720, as there are 6 letters with no repetition.
therfore probability of finding a word with vowels together is 144 / 720 = 1 / 5