Suppose there are two routes from North Point to Boulder Creek, four routes from Boulder Creek to Beaver Dam, four routes from Beaver Dam to Star Lake, and three routes directly from Boulder Creek to Star Lake. (Hint: Draw a sketch. Assume each route can pass through a city at most one time.) (a) How many routes from North Point to Star Lake pass through Beaver Dam? To answer this question, think of creating a route from North Point to Star Lake that passes through Beaver Dam as a 3-step process. Step 1: Choose a route from North Point to Boulder Creek Step 2: Choose a route from Boulder Creek to Beaver Dam. Step 3: Choose a route from Beaver Dam to Star Lake. There are 2 choices for step 1, 4 (b) How many routes from North Point to Star Lake bypass Beaver Dam? X choices for step 2, and 4 choices for step 3. Thus, the answer is 32