Solution
(a):If this problem needn't arrange all balls in a sequence.
3_balls:1/18424
4_balls:1/211876
5_balls:1/1906884
6_balls:1/13983816
(b):
The probability that get a special kind of prize is 1/44;
Without bonus
3_balls:1/18424
4_balls:1/211876
5_balls:1/1906884
With bonus
2+1_balls:1/51744
3+1_balls:1/810656
4+1_balls:1/9322544
5+1_balls:1/83902896