Sol. Let us name the rings as r 1 , r 2 , r 3 , r 4 and r 5 . The ring r 1 can be placed on any of the four fingers. Therefore, there are 4 ways to place the ring r 1 . After placing the ring r 1 , we have 5 choices for the ring r 2 , since for the finger which holds r 1 we have two choice to place r 2 , below or above r 1 . Similarly, r 3 (r 4 ) [r 5 ] can be placed in 6(7) [8] ways. Thus, the total number of ways to arrange five distinct rings on four fingers of the left hand is

(4) (5) (6) (7) (8) = 8!/3! = 6720.

Alternative Solution : Let us cut the fingers (mentally) and arrange them one after the other joining the adjacent fingers by three links. Now, the number of ways of arranging 5 rings on 4 fingers is equal to the number of ways arranging 5 rings and 3 identical links in a row. This can be done is 8!/3! = 6720 ways.