In a random arrangement of the letters of the word 'UNIVERSITY', what is the probability that two 1 's do not come together?

Step-by-step solution

The total number of arrangements of the letters of the word 'University' is 10! 2! as there are two i's. Regarding 2I's as one letter, number of ways of arrangement in which both I's are together =9 ! So, the number of ways in which 2I's are not together = 10! 2! -9 ! Hence, the required probability aligned & = 10! 2! -9! 10! 2! & =1- 2!9! 10! = 4 5 . aligned