How many paths are there and why?

A

andrev_markelov2020-11-09 17:01:33

Mathematics

andrev_markelov, 2020-11-09 17:01:33

If a walker starts at (0, 0) and goes to (50, 75) and has the constraint that each step goes either one unit up or one unit to the right, how many paths are there for such a walker... How many there are ways and why?

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W

Wataru, 2020-11-09
@andrev_markelov

The number of combinations from 125 to 50. Or 125!/50!/75!
Because he will definitely take 50 steps to the right and 75 steps up. In any order. Those. only 125 steps of which any 50 are horizontal.