Search any question & find its solution
Question:
Answered & Verified by Expert
The probability that in a random arrangement of the letters of the word 'UNIVERSITY', the two I's do not come together is
Options:
Solution:
2177 Upvotes
Verified Answer
The correct answer is:
$4 / 5$
$$
\begin{array}{l}
\because 1 \mathrm{U}, 1 \mathrm{~N}, 2 \mathrm{I}, 1 \mathrm{~V}, 1 \mathrm{E}, 1 \mathrm{R}, 1 \mathrm{~S}, 1 \mathrm{~T}, 1 \mathrm{Y} \\
\therefore \text { Total number of possible arrangements }=\frac{10 !}{2 !} \\
\text { and favourable arrangements }=\frac{10 !}{2 !}-9 ! \\
\therefore \text { Required probability }=\frac{\frac{10 !}{2 !}-9 !}{\frac{10 !}{2 !}} \\
=\frac{9 !(5-1)}{9 ! \times 10} \times 2=\frac{4}{5}
\end{array}
$$
\begin{array}{l}
\because 1 \mathrm{U}, 1 \mathrm{~N}, 2 \mathrm{I}, 1 \mathrm{~V}, 1 \mathrm{E}, 1 \mathrm{R}, 1 \mathrm{~S}, 1 \mathrm{~T}, 1 \mathrm{Y} \\
\therefore \text { Total number of possible arrangements }=\frac{10 !}{2 !} \\
\text { and favourable arrangements }=\frac{10 !}{2 !}-9 ! \\
\therefore \text { Required probability }=\frac{\frac{10 !}{2 !}-9 !}{\frac{10 !}{2 !}} \\
=\frac{9 !(5-1)}{9 ! \times 10} \times 2=\frac{4}{5}
\end{array}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.