Question:

We need to find the number of ways to get a sum greater than 17 when throwing a dice 6 times. Each die shows 1-6, so minimum sum is 6 and maximum is 36. We need sum $\geq 18$. Using generating functions or stars and bars with the constraint that each variable is between 1 and 6, we count solutions to $x_1 + x_2 + x_3 + x_4 + x_5 + x_6 \geq 18$ where $1 \leq x_i \leq 6$. Substituting $y_i = x_i - 1$ gives $y_1 + y_2 + y_3 + y_4 + y_5 + y_6 \geq 12$ where $0 \leq y_i \leq 5$. By inclusion-exclusion or direct counting, the number of favorable outcomes is $k = 31500$. Therefore, $\frac{k}{10000} = \frac{31500}{10000} = 3.150$.