The probability that in a random arrangement of the letters of the word 'UNIVERSITY' the two I's do not come together is

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 2 I's are not together = 10! 2! -9! Hence, the required probability = 10! 2! -9! 10! 2! =1- 2!9! 10! = 4 5 .