Find the probability that in a random arrangement of the letters of the word ‘SOCIAL’ vowels come together

Asked by Aaryan | 1 year ago |  63

##### Solution :-

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) =$$\dfrac{ n (E) }{ n (S)}$$

=$$\dfrac{ [4! × 3!] }{ 6!}$$

$$\dfrac{1}{5}$$

Answered by Aaryan | 1 year ago

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