JEE 2004 3D Geometry

here 6 permutations are possible as A corresponds to one of A',B',C'
and B corresponds to one of remaining A',B',C' and C corresponds to third of A',B',C'

therefore A lies on L₁, B lies on the line of intersection of P₁and P₂ and C lies on L₂ on the plane of P₂

therefore A' lies on L₂=C

B' lies on the line of intersection of P₁and P₂=B

C' lies on L₁ on the plane of P₁=A

i.e permutation of [A'B'C']=[ABC]