How many paths are there from the \(1\) at the top (in the ‘zeroth’ row) to the first \(70\), which appears in the middle of the eighth row?
These paths go down at each step to a number either to the left or to the right. An example is (the first \(1\)), \(1\), \(2\), \(3\), \(6\), \(10\), \(15\), \(35\) and then \(70\) to finish.