Find the probability that in a random arrangement of the letters of the word UNIVERSITY the two Is do not come together.

Options

A. `4//5`
B. `1//5`
C. `1//10`
D. `9//10`

Answer

A

Explanation

Total number of words formed by letters of UNIVERSITY
`= (10!)/(2!)` (`because` I is repeated)
Taking two `I_(S)` together, number of ways to arrange letters of UNIVERSITY = 9!
`therefore` Probability of two `I_(S)` coming together
`= (9!)/((10!)/(2!)) = (9 ! xx 2 !)/(10!) = 2/10 = 1/5`
`therefore` Probability of two `I_(S)` not coming together
`= 1 - 1/5 = 4/5`