Question

how many ways is rings of different type can be had in 4 fingers

Answer 1

Let us say there are 4 different rings available. There are four fingers. Each finger wears one ring.

So the number of different ways of wearing 4 different rings on 4 different fingers is = 4P4 = 4!  = 24.

Suppose the person wears only one ring : 
    the number of ways of wearing on 4 fingers = 4.

Suppose the person wears only two rings:
      number of ways of wearing on 4 fingers = 4P2 = 12

Suppose the person wears only three rings: 
     number of ways of wearing on 4 fingers: 4P3 = 24