Question
Find the probability that in a random arrangement of the letters of the word 'UNIVERSITY' the two I's come together.
Answer: Option D
The total number of words which can be formed by permuting the letters of the word 'UNIVERSITY' is $$\frac{{10!}}{{2!}}$$ as there is two I's.
Hence $$n(S) = \frac{{10!}}{{2!}}$$
Taking two I's as one letter, number of ways of arrangement in which both I's are together = 9!
$${\text{So}}\,n\left( X \right) = 9!$$
Hence required probability
$$\eqalign{
& = \frac{{n(X)}}{{n(S)}} \cr
& = \frac{{9!}}{{10!/2!}} \cr
& = \frac{1}{5} \cr} $$
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The total number of words which can be formed by permuting the letters of the word 'UNIVERSITY' is $$\frac{{10!}}{{2!}}$$ as there is two I's.
Hence $$n(S) = \frac{{10!}}{{2!}}$$
Taking two I's as one letter, number of ways of arrangement in which both I's are together = 9!
$${\text{So}}\,n\left( X \right) = 9!$$
Hence required probability
$$\eqalign{
& = \frac{{n(X)}}{{n(S)}} \cr
& = \frac{{9!}}{{10!/2!}} \cr
& = \frac{1}{5} \cr} $$
Was this answer helpful ?
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