Hm, before drawing number 3 there are 3 situations of ball combinations

8/55 ; 9/54 ; 10/53

after the draw

7/55 ; 8/54 ; 9/53 ; 10/52

where the first 3 have at least one colored ball

You have to somehow break the chance for each combination happening down.
Then you will see the systematics popping up.

Ok, I guess Im lost here too,

but Im not a math wiz, there are some math students here too,
please help out