Aptitude 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

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

\(=\dfrac{9!}{10!/2!}\)

\(=\dfrac{1}{5}\)

**Dipanjan**

*()
*

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.

www.lofoya.com/Aptitude-Questions-and-Answers/Permutation-and-Combination/l2p4

**Dipanjan**

*()
*

Taking two I's together..9factorial *2factorial..so ans will be 2/5

Since the letters are together (only 1 arrangement), no need to multiply by 2!. It will be 9! only.

As both are I, 2 factorial is not required.