Marvin the fly starts at (0,0). Each step, Marvin moves one unit right or one unit up. He is trying to get his home at (4,6). However, at (2,4) here is a frog that will eat him if he goes through that point. In how many ways can Marvin reach his home?
Marvin can reach his home in 8 different ways. He can go right 4 times and up 6 times, right 3 times and up 7 times, right 2 times and up 8 times, right 1 time and up 9 times, left 1 time and up 9 times, left 2 times and up 8 times, left 3 times and up 7 times, and left 4 times and up 6 times. He cannot go through (2,4) because of the frog.