Given that $1 \leq i,j \leq 6$ and that $1 \leq k \leq 12$, how many solutions there are given that $i+j>k$.
The problem appears when we have 2 players A and B. A using 2 dice (1 to 6 ) and B using one die (1 to 12). If the sum of the dice from player A respects $i+j>k$ then A won. If $i+j=k$ no one owns.
I've resolve it hard style, enumerating all the cases (from the 36 cases possibles for the sum of A) and I've found the answer. My problem is how can I use a more general rule for it.
I know I will have to use the stars-and-bars but I can't figure out out.
Any help/hint will be appreciated!