Problem #WSP-000397

Problems Algebra Pascal triangle

Problem

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.