The letter of word CLIFTON are placed at random in a row. What is the chance that two vowels come together?

Explanation

There are `7` letters in the word CLIFTON.

So, there are total `7!` ways of arranging these letters.

Now, we have to find number of ways that the two vowels come together.

We can consider these two vowels as a single entity as they will always be together.

So, we can arrange the word in `6!` ways.

When the two vowels `I` and `O` are together, we can arrange these vowels in `2!` ways.

So, there are total `6!xx2!` ways in which two vowels can come together.

`:.` The required probability `= (6!xx2!)/(7!) = 2/7.`