# Easy Probability Solved QuestionAptitude Discussion

 Q. Find the probability that in a random arrangement of the letters of the word 'UNIVERSITY' the two I's come together.
 ✖ A. 1/7 ✖ B. 3/5 ✖ C. 5/11 ✔ D. 1/5

Solution:
Option(D) is correct

The total number of words which can be formed by permuting the letters of the word 'UNIVERSITY' is $\dfrac{10!}{2!}$ as there is two I's.

Hence $n(S)=\dfrac{10!}{2!}$

Taking two I's as one letter, number of ways of arrangement in which both I's are together $= 9!$

So $n(X)=9!$

Hence required probability

$=\dfrac{n(X)}{n(S)}$

$=\dfrac{9!}{10!/2!}$

$=\dfrac{1}{5}$

## (4) Comment(s)

Dipanjan
()

As both are I, 2 factorial is not required.

Raina
()

I believe you are talking about $n(S)$. Here division by 2! s important. To know why is it important check explanation of this question.