Find the probability that in a random arrangement of the letters of the word UNIVERSITY the two I's do not come together.

Explanation

There are `10` letters in the word UNIVERSITY.

So, there are total `(10!)/(2!)` ways of arranging these letters as `I` comes twice in the word.

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

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

So, we can arrange the word in `9!` ways.



`:.` The probability two `I` are together `= (9!)/((10!)/(2!)) = 2/10 = 1/5.`

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