The letters of the word SOCIETY are placed at random in a row. The probability that the three vowels come together is?

\frac{1}{6}

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\frac{1}{7}

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\frac{2}{7}

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\frac{5}{6}

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Solution

The correct option is B $\frac{1}{7}$
$\begin{matrix} S O C I E T Y a r e p l a c e d a t r a n d o m i n a r o w T h e n v o w e l s c o m e t o g e t h e r i s L e t t h r e e v o w e l s a r r a n g e i n a r o w b y 3! = 3 \times 22 = 6 w a y . W e c o m b i b e t h r e e v o w e l s t o f o r m o n e l e t t e r t h e n, (O E I), S C T Y . T h e n, a r r a n g i n g i n 5! = 5 \times 4 \times 3 \times 2 = 120 w a y . P r o b a b i l i t y o f 3 v o w e l s c o m e t o g e t h e r = \frac{120 \times 6}{7 \times 6 \times 3 \times 4 \times 3 \times 2 \times 1} = \frac{1}{7} A n s . \end{matrix}$

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