Question 1026650
<pre>

                    A 

                  L   L 

                G   G   G

              E   E   E   E

            B   B   B   B   B

              R   R   R   R

                A   A   A

                  I   I

                    C 

Look at a sample path:

                    A 
                   /
                  L   L 
                   \
                G   G   G
                     \
              E   E   E   E
                       \
            B   B   B   B   B
                       /
              R   R   R   R
                     /
                A   A   A
                     \
                  I   I
                     /
                    C 

That particular path could be represented by LRRRLLRL.

Or you could stay along one of the edges:


                    A 
                   /
                  L   L 
                 /
                G   G   G
               /
              E   E   E   E
             /
            B   B   B   B   B
             \
              R   R   R   R
               \
                A   A   A
                 \
                  I   I
                   \
                    C 

That path could be represented by LLLLRRRR

Every path could be represented by a distinguishable 
permutation of LLLLRRRR.  And every distinguishable
permutation of LLLLRRRR would represent a different
path.

You can look at that either of two ways:

The number of distinguishable permutations of LLLLRRRR
and calculate it this way:

So the answer is  {{{8!/(4!4!)}}}{{{""=""}}}{{{40320/(24*24)}}}{{{""=""}}}{{{70}}} possible paths.

Or we could say there are 8 positions in each distinguishable
permutation of LLLLRRRR, and we choose 4 or those positions to
place the L's in in 8C4 ways and the other 4 would be filled 
with R's in only 1 way.  So the answer in that case would be
simply the combinations of 8 things taken 4 at a time.

8C4 = 70.

Edwin</pre>