Suppose there are two routes from North Point to Boulder Creek, four routes from Boulder Creek to Beaver Dam, four routes from

Question

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
Step 2: Choose a route from 
Step 3: Choose a route from Beaver Dam to Star Lake.
There are 2__choices for step 1, 4__to Beaver Dam.
(b) How many routes from North Point to Star Lake bypass Beaver Dam?

choices for step 3. Thus, the answer is 32

Kunduz · Accepted Answer

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