Find the probability that in a random arrangement of the letters of the word 'UNIVERSITY' the two I's come together.

Answer: Option D

The total number of words which can be formed by permuting the letters of the word 'UNIVERSITY' is $$\frac{10!}{2!}$$ as there is two I's.
Hence $$n(S)=\frac{10!}{2!}$$
Taking two I's as one letter, number of ways of arrangement in which both I's are together = 9!
$$\text{So}n\left(X\right)=9!$$
Hence required probability
$$\begin{array}{rl}& =\frac{n(X)}{n(S)}\\ & =\frac{9!}{10!/2!}\\ & =\frac{1}{5}\end{array}$$