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Question
The letters of the word' CLIFTON' are placed at random in a row. What is the chance that two vowels come together?
Solution
There are 7 letters in the word ‘CLIFTON’, which can be arranged in 7! ways.
There are two vowels, namely I and O.
Let us consider these two vowels as one letter.
So, when the two vowels are clubbed together, we have (I,O) CLFTN.
We can arrange six letters in a row in 6! ways.
Also, the two vowels can be arranged in 2! ways.
Hence, required probability = \[\frac{6! \times 2!}{7!} = \frac{6! \times 2}{7 \times 6!} = \frac{2}{7}\]
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