14.6. How many different paths exist on a plane leading from a point with coordinates ( $0, n$ ) to a point with coordinates ( $m, m$ ), if it is allowed to move each time either 1 up (coordinate $y$ increases by 1), or 1 left (coordinate $x$ decreases by 1)?
14.6. Answer: $C_{n}^{m}$. In total, we need to make $m$ steps up and $n-m$ steps to the left. Therefore, out of $n$ steps, we need to choose $m$ steps up.