Top Dice (noch nicht übersetzt)

There are 1111 ways in which five 6-sided dice (sides numbered 1 to 6) can be rolled so that the top three sum to 15. Some examples are:

D₁,D₂,D₃,D₄,D₅ = 4,3,6,3,5
D₁,D₂,D₃,D₄,D₅ = 4,3,3,5,6
D₁,D₂,D₃,D₄,D₅ = 3,3,3,6,6
D₁,D₂,D₃,D₄,D₅ = 6,6,3,3,3

In how many ways can twenty 12-sided dice (sides numbered 1 to 12) be rolled so that the top ten sum to 70?