2 added output
source | link

You could try something like this:

Show[Graphics[{RandomColor[], Line[#]}] & /@ ( (* Make graphics of *)
FoldList[Plus, RandomReal[{0, 0.1}, 2] + {0, 0}, #] & /@ (* Trajectories built from *)
Permutations[ (* All possible orderings of *)
    Join @@ ({{0, 1}, {1, 0}} & /@ Range[5]) (* Five steps N and five steps E*)
   ]
)]

The RandomReal[{0,0.1},2] is a random near-the-origin starting location, just to offset the different lines from one another visually.

enter image description here

You could try something like this:

Show[Graphics[{RandomColor[], Line[#]}] & /@ ( (* Make graphics of *)
FoldList[Plus, RandomReal[{0, 0.1}, 2] + {0, 0}, #] & /@ (* Trajectories built from *)
Permutations[ (* All possible orderings of *)
    Join @@ ({{0, 1}, {1, 0}} & /@ Range[5]) (* Five steps N and five steps E*)
   ]
)]

The RandomReal[{0,0.1},2] is a random near-the-origin starting location, just to offset the different lines from one another visually.

You could try something like this:

Show[Graphics[{RandomColor[], Line[#]}] & /@ ( (* Make graphics of *)
FoldList[Plus, RandomReal[{0, 0.1}, 2] + {0, 0}, #] & /@ (* Trajectories built from *)
Permutations[ (* All possible orderings of *)
    Join @@ ({{0, 1}, {1, 0}} & /@ Range[5]) (* Five steps N and five steps E*)
   ]
)]

The RandomReal[{0,0.1},2] is a random near-the-origin starting location, just to offset the different lines from one another visually.

enter image description here

1
source | link

You could try something like this:

Show[Graphics[{RandomColor[], Line[#]}] & /@ ( (* Make graphics of *)
FoldList[Plus, RandomReal[{0, 0.1}, 2] + {0, 0}, #] & /@ (* Trajectories built from *)
Permutations[ (* All possible orderings of *)
    Join @@ ({{0, 1}, {1, 0}} & /@ Range[5]) (* Five steps N and five steps E*)
   ]
)]

The RandomReal[{0,0.1},2] is a random near-the-origin starting location, just to offset the different lines from one another visually.