A: Do you know the "balls and boxes" or "divider" technique?

Basically, we subtract 1 from each number so that C,A,R,D are nonnegative integers with C+A+R+D = 31. Now we have 31 units and three "dividers" to split with. Any permutation of the 31 units and three dividers results in four numbers C,A,R,D such that C+A+R+D = 31. The total number of ways is .

B: Let C = 32, find the number of ways such that A+R+D = 2. Multiply by 4 to account for A = 32, etc.