Probability Help (die problem) A die is rolled 20 times. How many different sequences 
a) each number 1-6 is rolled exactly three times
My Answer: (20 choose 6)*(3 choose 1)
b) each number 1-6 are each rolled exactly once in the first six rolls?
My Answer: (20 choose 6)*(6 choose 1)
c) each number rolled is at least as big as the number that was rolled directly before it?
ex: 111222333344455566666
My Answer: No idea

There is sort of a solution to c. It is preposterously long and cumbersome, maybe it will help to find something shorter.
$\sum _{a=1}^z \sum _{b=a}^z \sum _{c=b}^z \sum _{d=c}^z ...\sum _{q=p}^z \sum _{r=q}^z \sum _{s=r}^z \sum _{t=s}^z 1$
when z = 6 we get 53130.
