The total number of positive integral solutions of $15 < x_1+x_2+x_3 \leq 20$ is equal to:
Step-by-Step Solution
Key Concept: Count positive solutions for each value: for $x_1+x_2+x_3=n$ (positive integers), number of solutions $=\binom{n-1}{2}$. Sum for $n=16,17,18,19,20$.
Total $=\mathbf{685}$. Answer: A.
Correct Answer: A