Question 462945
1st rout
a
[x][x][x]b[][]
--[][][][x][]
--[][][][x][]
--[][][][x][]
--[][][][x[x]c
          
2nd rout
a
[x][x][x]b[][]
--[][][][x][]
--[][][][x][]
--[][][][x][x]
---[][][][][x]c
          
3rd rout
a
[x][x][x]b[][]
--[][][][x][]
--[][][][x][x]
---[][][][][x]
---[][][][][x]c


4th  rout
a
[x][x][x]b[][]
---[][][][x][x]
----[][][][][x]
----[][][][][x]
----[][][][][x]c
          

since one can move only down or to the right, there is 4 different routes start at A, pass through B, and end at C