Page 88 problem 5
There are three different routes connecting city A to city B. How many ways can a round trip be made from A to B and back? How many ways if it is desired to take a different route on the way back?
We have 3 different routes connecting the 2 cities A and B.
Each trip is the event and on each trip we have 2 choices:
1.) The route we take on the way there
2.) The route we take on the way back
Since we have 3 total routes and 2 choices to make this means there are \(3^2=9\) possible ways a round trip can be made from A to B.
We can also just list out all the possible routes to get the same answer:
\((1,1), (1,2), (1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3) = 9\) ways
For part 2 if we are taking a different route back this just means we have 3 ways to choose the first route and 2 ways to pick the route back.
\(3 x 2=6\) ways to make the trip with a different route on the way back.
We can also just list out all the possible ways taking a different route we just dont include \((1,1),(2,2),(3,3)\)
\((1,2),(1,3),(2,1),(2,3),(3,1),(3,2)\)