My crazy die has one side with one pip on it, two with two pips , and three on each of three remaining sides.

I tossed it 7 times in a row and wrote down the result of those tosses as a 7 digit number.

What is the probability that this number

a. Is bigger than 1231111?

b. Contains at least one triplet of identical digits?

c. Is divisible by 3?

d. Exhibits all the 3 features mentioned above?