Graphs Problem 1

Solution

Any path from a to b must go through r and w. There are four paths from a to r: apr, aqr, apqr, and aqpr. Similarly, there are four paths from w to b. Finally, there are three paths from r to w: rw, rsw, and rtw. So we have $$4 \cdot 3 \cdot 4 = 48$$ paths from a to b.