Question

There are five students S1,S2,S3,S4 and R5 arranged in a row, where initially the seat R1is allotted to the students are randomly allotted the five seats R1,R2,R3,R4 and R6 arranged in a row, where initially the seat Ri is allotted to the student Sii,=1,2,3,4,5.But,ontheexaminS_(1) gets the previously allotted seat R_(1), 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)` Select the correct answer from above options

Answer 1

Correct Answer - A 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 seat is 4! (1- (1)/(1!) +(1)/(2!) -(1)/(3!) +(1)/(4!))=24(1-1+(1)/(2)-(1)/(6)+(1)/(24))=24((12-4+1)/(24))=9 :. Required probability =(9)/(!20)=(3)/(40)