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With four states there are 2^4 =16 transitions are possible .

For each transitions, there are 4 possibilities 1) no transition 2) transition on input a 3)transition on input b 4) transition with a or b both (assuming no epsilon move)

As there are total 16 possible transition Therefore total 4^16 diagrams will be possible .For each diagram we can have ( 1 , 2, 3 or 4 final states)I.e for each diagram we have (4c1+4c2+4c3+4c4) choices for final states . 

Out of which we can remove following cases

1)all four states are disconnected

2)only 2 states are connected 

3)only 3 connected states 

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