Heads you lose, tails I win

Extract

The array shown in the diagram, where each integer appearing shows the number of routes to that point, assuming there is a North-South wall that cannot be crossed, but otherwise constructed using the same one-step, no back-tracking rules as in the production of Pascal’s triangle, may be used as the starting point of an interesting investigation, provided one’s pupils know a bit about combinations, the binomial theorem and discrete probability distributions.