Given is The word ‘SOCIAL’.
By using the formula of probability, we get,
P (E) = favourable outcomes / total possible outcomes
In the random arrangement of the alphabets of word “SOCIAL” we have to find the probability that vowels come together.
Total possible outcomes of arranging the alphabets are 6!
n (S) = 6!
Let E be the event that vowels come together
Number of vowels in SOCIAL is A, I, O
So, number of ways to arrange them where, (A, I, O) come together
n (E) = 4! × 3!
P (E) = n (E) / n (S)
= [4! × 3!] / 6!
= 1/5