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The letters of SOCIETY are placed at ran...

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

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There are 7 letters in the word 'SOCIETY'. These 7 letters can be arranged in 7! Ways.
. `therefore` Totol number of possible elementary events = 7!
Now, three vowels (i.e., O, I and E) should occur together,
`therefore` We can consider all the three vowels as a single unit.
So, 5 letters cna be arranged in 5! ways.
Also, the three vowels O, I and E can be put together in 3! ways.
Therefore, the total number of arrangements in which three vowels occurs together is `5!xx3!`
Hence, required probability = `(5!xx3!)/(7!)=(1)/(7)`.
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