Step 1: Understanding the Question:
We need to logically arrange the four parts P, Q, R, and S to make a complete, grammatically sound sentence.
Step 2: Key Formulas and approach:
1. Identify the primary subject, which here uses the correlative conjunction "neither... nor".
2. Find prepositional modifiers that belong to the subject.
3. Find the verb phrase and the corresponding infinitive phrase.
Step 3: Detailed Explanation:
$\bullet$ Fragment R: "neither the principal nor the bursar" is the subject of the sentence.
$\bullet$ This subject is modified by the prepositional phrase in Fragment P: "of the college was willing". This creates a singular verb structure "was willing" that agrees with "neither... nor". This gives R $\rightarrow$ P.
$\bullet$ The adjective "willing" is idiomatically followed by an infinitive phrase starting with "to". Fragment S: "to accept responsibility for" naturally follows "was willing". This gives R $\rightarrow$ P $\rightarrow$ S.
$\bullet$ The preposition "for" in Fragment S must have a noun phrase as its object. Fragment Q: "the administrative failure" fits perfectly as the object. This gives the sequence R $\rightarrow$ P $\rightarrow$ S $\rightarrow$ Q.
Step 4: Final Answer:
The correct order is RPSQ, which is Option (A).