In a shooting competition, three targets are set as shown:

Target (I) has four rings on which a person can hit in order from inside to outside. Target (II) has three rings on which a person can hit in order from outside to inside. Target (III) has five rings on which a person can hit in order from inside to outside. The number of ways in which 12 shots (one at each ring) can be made: [Hint: Any target can be chosen before not completing specific target but order of hit for a particular target should be as specified above in condition.]

Options

A. `(12!)/(4!xx3!xx5!)`
B. `(12!)/(4!xx3!xx5!)`
C. `""^(12)C_(4)""^(8)C_(3)'""^(5)C_(5)`
D. 12!

Answer

A, C