### Counting Trails

48 Charlotte Math Meetup students have a meetup together. Each holds a square tile of 1 m

^{2}. They put the tiles together to form a big rectangle of 48 m^{2}. Leo tries to complete a trail from the bottom left tile to the top right tile. (The trails are not along the edges of the tiles, but from one tile to another tile.) If every time he can only go up or right, and if the students try to make the rectangle such that there are as many trails as possible. what’s the most number of trails?