We have 10 letters word “UNIVERSITY”. So, the arrangement of 10 things can be done in 10! ways. But, two I’s are repeating. So, the arrangement can be done in
10!
2!
=5×9! Number of ways of arrangement that the two I’s do not come together = Total number of arrangement – number of arrangement in which both I’s are together. Number of arrangements in which both I’s are together: We consider both I’s as one letter. Therefore, we now have 9 letters. So the number of arrangement = 9! ∴ Number of ways of arrangement that the two I’s do not come together = 5 × 9! – 9! =4×9! So, the required probability =