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Case I: 1 three times, other 3 distinct numbers

0 included in 3 distinct numbers

C(8,2)(6!/3!-5!/3!) (subtraction is due to 0 occupying the first place)

0 not included in 3 distinct numbers

C(8,3)6!/3!

Cases II to IX will be similar to case I

Case X: 0 three times, other 3 distinct numbers

C(9,3)6!/3!-5!/2!