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Suppose you take route 2 from A to B then you can continue in 5 ways to get 5 routes from A to C,
Continuing you can see that each of the 4 routes from A to B generates 5 routes from A to C. Hence there are 4 × 5 = 20 routes from A to C. Each one of these can be extended to a route to D in how many ways? How many routes are there from A to D? Penny Kapilan replied
For each of the 20 routes from A to C in how many ways can it be extended to a route from A to D? How many possible routes are there from A to D? When you arrive at D you have used one route in each of the three legs of the trip. Thus on the way back you have one less route to choose from in each of the three legs. Penny  


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