Step 1: Find the main subject.
Neither the principal nor the bursar (R) is the main subject of the sentence. This is a negative subject using neither-nor.
Step 2: Build the sentence logically.
After the subject (R) comes of the college was willing (P), followed by to accept responsibility for (S), and finally what they refused responsibility for: the administrative failure (Q).
Step 3: Arrange in order.
The correct sequence is R + P + S + Q, forming a complete and coherent sentence about accountability.
\[ \boxed{\text{RPSQ}} \]