Probability
Aptitude

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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

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

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

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


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