Question

The probability that in a random arrangement of the letters of the word $UNIVERSITY$ the $2$ Is do not come together is

• A. $\frac{3}{5}$
• B. $\frac{4}{5}$
• C. $\frac{5}{6}$
• D. $\frac{2}{5}$

Answer 1

The correct option is B $\frac{4}{5}$

$|U|N|V|E|R|S|T|Y|$
We could put 2 $I$s together at 9 places, selection of a place out of 9 ${=}^9{C}_1$
Then we could arrange it in $8!$ ways
Probability when 2 $I$s do not come together$=1-$Probability when 2 $I$s come together
Probability when 2 $I$s come together$=\frac{{}^9{C}_1\times 8!}{\frac{10!}{2!}}=\frac{1}{5}$
Probability when 2 $I$s do not come together$=1-\frac{1}{5}=\frac{4}{5}$