CAT 2017 Quantitative Ability

Since rings are distinct, hence they can be named as ${\mathit{R}}_1,{\mathit{R}}_2,{\mathit{R}}_3$ and ${\mathit{R}}_5$
The ring ${\mathit{R}}_1$, can be placed on any of the four fingers in 4 ways
The ring ${\mathit{R}}_2$ can be placed on any of the four fingers in 5 ways
since the finger in which ${\mathit{R}}_1$, is placed now has 2 choices, one above the ${\mathit{R}}_1$, and one below the ring ${\mathit{R}}_1$,
Similarly ${\mathit{R}}_3$, ${\mathit{R}}_4$ and ${\mathit{R}}_5$can be arrange in 6, 7 and 8 ways respectively
Hence, the required number of ways = $4\times 5\times 6\times 7\times 8=6720$