42) A mapping is selected at random from the set of all mappings of the set A = (1, 2,...., n) into itself. The probability that the mapping selected is bijective,  is
( a )   1 n   !   ( b )   1 n n ( c )   n   ! 2 n ( d )   n   ! n n

Dear Student,
Please find below the solution to the asked query:

Mapping is defined from A to A.A=1,2,3,...,nEach element of Ahas options in codoain to be mapped, henceTotal mappings=n×n×n×.. ntimes=nnFor one-one each element must have uinque image in codomainFirst element of A has n options, second has n-1 options, third hasn-2 options,...., last has 1 option.Hence Number of one-one functions=n×n-1×n-2×......×1=n!Now as number of elements in domain= number of elements in codomain,hence total one-one functions=Total onto functions.Hence yotal bijectiveone-one and onto functions=n!Required Probability=n!nn Answer 

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