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

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
$$\eqalign{ & = \frac{{n(X)}}{{n(S)}} \cr & = \frac{{9!}}{{10!/2!}} \cr & = \frac{1}{5} \cr} $$