SATHEE: Probability 2 Question 16

Probability 2 Question 16

16. 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) $\frac{1}{8}$

(d) $\frac{1}{5}$

Show Answer

Solution:

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 $R_{5}$

$∴$ Total number of arrangement of sitting five students is $5! = 120$

Here, $S_{1}$ gets previously alloted seat $R_{1}$

$∴ S_{2}, S_{3}, S_{4}$ 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

$\begin{aligned} 4! 1 - \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} & = 241 - 1 + \frac{1}{2} - \frac{1}{6} + \frac{1}{24} \\ = 24 \frac{12 - 4 + 1}{24} = 9 \end{aligned}$

$∴$ Required probability $= \frac{9}{120} = \frac{3}{40}$

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Probability 2 Question 16

16. The probability that, on the examination day, the student S1 gets the previously allotted seat R1, and

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16. The probability that, on the examination day, the student $S_{1}$ gets the previously allotted seat $R_{1}$ , and