The word 'UNIVERSITY' is arranged randomly. T | vedclass

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(C) The word '$UNIVERSITY$' contains $10$ letters,where '$I$' appears $2$ times and all other letters are distinct.Total number of arrangements $ = \f

Vedclass · Accepted Answer

$\frac{4}{5}$

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(C) The word '$UNIVERSITY$' contains $10$ letters,where '$I$' appears $2$ times and all other letters are distinct.Total number of arrangements $ = \frac{10!}{2!}$.To find the probability that both '$I$'s come together,we treat the two '$I$'s as a single unit $(II)$. Now we have $9$ units to arrange: $(U, N, V, E, R, S, T, Y, (II))$.The number of ways to arrange these $9$ units is $9!$.Probability that both '$I$'s come together $ = \frac{9!}{\frac{10!}{2!}} = \frac{9! 	imes 2!}{10!} = \frac{2}{10} = \frac{1}{5}$.Therefore,the probability that both '$I$'s do not come together $ = 1 - \frac{1}{5} = \frac{4}{5}$.

The word '$UNIVERSITY$' is arranged randomly. Then the probability that both '$I$'s do not come together is:

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