If the letters of the word "UNIVERSITY" are a | vedclass

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(C) The total number of letters in the word "$UNIVERSITY$" is $10$. The letter '$I$' appears $2$ times.The total number of arrangements is $\frac{10!}

Vedclass · Accepted Answer

$4$

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(C) The total number of letters in the word "$UNIVERSITY$" is $10$. The letter '$I$' appears $2$ times.The total number of arrangements is $\frac{10!}{2!}$.To find the probability that both '$I$'s come together,we treat the two '$I$'s as a single unit. Now we have $9$ units to arrange,which can be done in $9!$ ways.The probability that both '$I$'s come together is $P(	ext{together}) = \frac{9! 	imes 2!}{10!} = \frac{2}{10} = \frac{1}{5}$.The probability that both '$I$'s do not come together is $1 - P(	ext{together}) = 1 - \frac{1}{5} = \frac{4}{5}$.

If the letters of the word "$UNIVERSITY$" are arranged at random,what is the probability that both '$I$'s do not come together (in $/5$)?

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