The diagram above shows the various paths along…
A good way to solve this problem is to use the idea of the fundamental counting principle. In a more standard form you could be asked a question, such as if Tom as 3 belts, 4 ties, and 6 shirts, how many outfits could he make with those items? We can consider each item a decision point, i.e., belts, ties, and shirts. To solve this, we just need to multiply the number of decisions Tom can make together, so:
3 x 4 x 6 = 72 ways.
Tom has 72 options when dressing with those items.
The same logic can be applied to this problem. We first determine the number of ways the mouse can go from one point to the next. Notice we added in “decision points” to our diagram.
X to P1 = 1
P1 to P2 = 2
P2 to P3= 1
P3 to P4= 2
P4 to P5= 1
P5 to P6 = 3
P6 to Y = 1
Therefore, to determine the total number of ways from X to Y, we multiply all these numbers together:
1 x 2 x 1 x 2 x 1 x 3 x 1 = 12 ways.
There are 12 different paths.