Five people P,Q,R,S,T sit in a row. Exactly one person separates Q and R, and S cannot sit adjacent to Q. How many distinct arrangements satisfy both conditions?
Number the seats1–5. For Q in seats1,2,3,4,5, R can occupy a seat two away. The corresponding counts after placing S away from Q are4,2,4,2,4: for example Q=1 forces R=3 and leaves two permitted seats for S, with P/T in2! orders. Sum4+2+4+2+4=16, D.
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