Marvin the fly is attempting to reach his home at coordinates (4,6) from (0,0) by moving either right or up. He must avoid the point (1,4) where a frog is located. The document seeks to determine the number of valid paths Marvin can take to avoid the frog.

1. Marvin the fly starts at (0,0). Each step, Marvin moves one unit right or one unit up. He is trying to
get to his home at (4,6). However, at (1,4), there is a frog that will eat him if he goes through that
point. In how many ways can Marvin reach his home?