Since rings are distinct, hence they can be named as R1,R2,R3 and R5 The ring R1, can be placed on any of the four fingers in 4 ways The ring R2 can be placed on any of the four fingers in 5 ways since the finger in which R1, is placed now has 2 choices, one above the R1, and one below the ring R1, Similarly R3, R4 and R5can be arrange in 6, 7 and 8 ways respectively Hence, the required number of ways = 4×5×6×7×8=6720