Fundamental Principle Of Counting

Case-I : when exactly one box provides four balls ( 3R1B or 2R2B )
Number of ways in this case
Case-II : when exactly two boxes provide three balls ( 2R1B or 1R2B ) each
Number of ways in this case
Required number of ways =21816
Language ambiguity : If we consider at least one red ball and exactly one blue ball, then required number of ways is 9504 . None of the option is correct.
The correct option is (A): 21816