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

A. $$\frac{1}{7}$$

B. $$\frac{3}{5}$$

C. $$\frac{5}{11}$$

D. $$\frac{1}{5}$$

Answer: Option D

Solution(By Examveda Team)

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