Given: The word ‘SOCIAL’.
By using the formula,
P (E) =\(\dfrac{ favourable \;outcomes }{ total \;possible\; outcomes}\)
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) =\( \dfrac{ n (E) }{ n (S)}\)
=\(\dfrac{ [4! × 3!] }{ 6!}\)
= \(\dfrac{1}{5}\)
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