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

Probability that the two 'I's do not come together in an arrangement of 'UNIVERSITY' The word 'UNIVERSITY' contains 10 letters with 'I' appearing twice; all other letters are unique. The total number of distinct arrangements is given by 10! 2! = 1,814,400 . Treating the two 'I's as a single block yields 9 distinct units. The number of arrangements where the 'I's are together is 9! = 362,880 . The complementary probability approach gives: P( 'I's not together ) = 1 - P( 'I's together ) = 1 - 9! 10! 2! = 1 - 2 10 = 4