Chapter 1.1, Problem 20PS

The ferry portion on the USS Nimitz, houses $10$ rows of parking spaces. Repeat Problem $19$ for $10$ rows instead of four.

Problem 19:

A car pulls onto the USS Nimitz, which is now a car ferry.

As a car enters the ferry, there are four rows of traffic directors arranged in a triangular pattern, such that one director is in the first row, two in the second, three in the third, and four in the fourth row. They are directing traffic into five parking spots, labelled A through E in Figure 1.7

FIGURE 1.7 Traffiic directors lead cars to spaces.

Given that cars must proceed according to the traffic arrows, how many different paths are there into each of the parking spots?