An ant crawls along a coordinate grid. The ant starts at \((0,0)\). At each step, the ant either moves up one unit (with probability 1/2) or to the right 1 unit (with probability 1/2).
After 5 steps the ant has
- a 5/32 chance of being at the coordinate \((4,1)\),
- a 10/32 chance of being at the coordinate \((3,2)\), and
- a 17/32 chance of being at one of the coordinates \((2,3), (1,4), (5,0), (0,5)\)
What is the probability that the ant is at position \((4,2)\) after 6 steps?