Ok, so we've got twelve balls all marked with a distict number between 1 and 12.

( 1 ) ( 2 ) ( 3 ) ( 4 ) ( 5 ) ( 6 ) ( 7 ) ( 8 ) ( 9 ) (10) (11) (12)

In how many ways can we pick three balls from the twelve so that the difference between the numbers written on them is at least 2.

For example: we are not allowed to pick ( 1 ) ( 2 ) ( 5 ) since 2-1=1, but are allowed to choose ( 1 ) ( 5 ) (12).

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The answer should be 120, but why?