There is a rectangular lake that people need to cross to get from village $A$ to village $B$.
This is a rather abstract lake with size $6\times 4$. Every winter it freezes over and will always have $5$ holes. These are not located at point $A (1,1)$ or point $B(6,4)$ and cannot stack on top one another, i.e. if hole 1 is at $(1,2)$ then hole 2 cannot be on the same location $(1,2)$.
What is the probability that the holes will form a complete blockage so the lake cannot be crossed from $A$ to $B$.
Examples:
I will write Entrance/Exit as e, ice as x and hole as o.
Example 1:
e x x o x x
x x x o x x
x x x o x x
x x x o o e
this lake is unpassable.
Example 2:
e x x x x x
o o o o x x
x x o x x x
x x x x x e
this lake is passable.