Gino wants to travel from home to school. Find how many routes are possible if he does not travel in a northerly direction.
To find the number of routes Gino can take from home to school without traveling in a northerly direction, we can use the concept of permutations.
Let's assume that Gino's home is located at point A and his school is located at point B. Since Gino cannot travel in a northerly direction, we can assume there are only three possible directions he can take: east, west, and south.
If we consider each direction as a distinct step, we can calculate the number of permutations of these steps to find the total number of routes.
1. East: Let's say Gino takes the eastern direction. He needs to calculate the number of permutations of the remaining two steps (west and south). This can be done using the formula for permutations:
P(2, 2) = 2! = 2.
So, there are 2 routes when Gino travels east.
2. West: Similarly, if Gino travels west as the first step, he also needs to calculate the number of permutations of the remaining two steps (east and south).
P(2, 2) = 2!.
This will also give us 2 routes when Gino travels west.
3. South: Finally, if Gino takes the southern direction as the first step, again, he needs to calculate the number of permutations of the remaining two steps (east and west).
P(2, 2) = 2!.
This will also yield 2 routes when Gino travels south.
To find the total number of routes, we need to add up the number of routes for each direction:
Total routes = routes when traveling east + routes when traveling west + routes when traveling south
= 2 + 2 + 2
= 6.
Therefore, there are 6 possible routes for Gino to travel from home to school without traveling in a northerly direction.