PARAGRAPH "A" There are five students S1, S2, S3, S4 and S5 in a music class and for them there are five seats R1, R2,R3,R4 and R5 arranged in a row, where initially the seat Ri is allotted to the student Si, i=1,2,3,4,5. But, on the examination day, the five students are randomly allotted the five seats. Question:The probability that, on the examination day, the student S1 gets the previously allotted seat R1, and NONE of the remaining students gets the seat previously allotted to him/her is

Question

PARAGRAPH "A" There are five students S1, S2, S3, S4 and S5 in a music class and for them there are five seats R1, R2,R3,R4 and R5 arranged in a row, where initially the seat Ri is allotted to the student Si, i=1,2,3,4,5. But, on the examination day, the five students are randomly allotted the five seats. Question:The probability that, on the examination day, the student S1 gets the previously allotted seat R1, and NONE of the remaining students gets the seat previously allotted to him/her is (A) (3/40) (B) (1/8) (C) (7/40) (D) (1/5)

Tardigrade Admin · Accepted Answer

Required probability =(4 !((1/2 !)-(1/3 !)+(1/4 !))/5 !) =(9/120)=(3/40)

$\frac{3}{40}$

$\frac{1}{8}$

$\frac{7}{40}$

$\frac{1}{5}$

Required probability $= \frac{4 ! ( \frac{1}{2 !} - \frac{1}{3 !} + \frac{1}{4 !} )}{5 !}$
$= \frac{9}{120} = \frac{3}{40}$

403​

81​

407​

51​

Required probability =5!4!(2!1​−3!1​+4!1​)​ =1209​=403​

$\frac{3}{40}$

$\frac{1}{8}$

$\frac{7}{40}$

$\frac{1}{5}$

Required probability $= \frac{4 ! ( \frac{1}{2 !} - \frac{1}{3 !} + \frac{1}{4 !} )}{5 !}$
$= \frac{9}{120} = \frac{3}{40}$