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
=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
=| number of arrangements two I' snot together |
| total number of arrangemets |
= =4∕5