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 only visit a city at most one time.)(a)How many routes from North Point to Star Lake pass through Beaver Dam?Incorrect: Your answer is incorrect.(b)How many routes from North Point to Star Lake bypass Beaver Dam?

Answer 1

Answer:

(a)32 Routes

(b)6 routes

Step-by-step explanation:

The sketch of the route is attached below

If an operation takes j steps, where the first step can be performed in $n_1$ ways, the second step takes $n_2$ ways and the jth step can be performed in $n_j$ ways,

then the operation can be performed in: $n_1n_2...n_j \: ways$.

(a)Number of Routes from North Point to Star Lake pass through Beaver Dam.

Number of routes from North Point to Boulder Creek=2

Number of routes from Boulder Creek to Beaver Creek=4

Number of routes from Beaver Creek to Star Lake=4

Number of Routes from North Point to Star Lake pass through Beaver Dam=2X4X4=32 routes

(b)Number of routes from North Point to Star Lake which bypass Beaver Dam.

Number of routes from North Point to Boulder Creek=2

Number of routes from Boulder Creek directly to star Lake=3

Number of routes from North Point to Star Lake which bypass Beaver Dam=2X3 =6 routes