Probability
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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

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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.

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


Raina
 ()

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