Probability Ques 37
Pragraph Based Questions
There are five students $S _1, S _2, S _3, S _4$ and $S _5$ in a music class and for them there are five seats $R _1, R _2, R _3, R _4$ and $R _5$ arranged in a row, where initially the seat $R _i$ is allotted to the student $S _i, i=1,2,3,4,5$. But, on the examination day, the five students are randomly allotted the five seats.
(There are two questions based on Paragraph, the question given below is one of them)
(2018 Adv.)
The probability that, on the examination day, the student $S _1$ gets the previously allotted seat $R _1$, and NONE of the remaining students gets the seat previously allotted to him/her is
(a) $\frac{3}{40}$
(b) $\frac{1}{8}$
(c) $\frac{7}{40}$
(d) $\frac{1}{5}$
Show Answer
Answer:
Correct Answer: 37.(a)
Solution:
Formula:
- Here, five students $S _1, S _2, S _3, S _4$ and $S _5$ and five seats $R _1, R _2, R _3, R _4$ and $R _5$
$\therefore$ Total number of arrangement of sitting five students is $5 !=120$
Here, $S _1$ gets previously alloted seat $R _1$
$\therefore S _2, S _3, S _4$ and $S _5$ not get previously seats.
Total number of way $S _2, S _3, S _4$ and $S _5$ not get previously seats is
$ \begin{aligned} 4 ! (1-\frac{1}{1 !}+\frac{1}{2 !}-\frac{1}{3 !}+\frac{1}{4 !} )& =24(1-1+\frac{1}{2}-\frac{1}{6}+\frac{1}{24}) \\ & =24 (\frac{12-4+1}{24})=9 \end{aligned} $
$\therefore$ Required probability $=\frac{9}{120}=\frac{3}{40}$
BETA
