1. Show that each row of Pascal's triangle begins with a 1 in the left-most position and n in the next position to the right, where n is the number of rows from the top.
2. Explicitly compute the number of paths too the points marked F, G, and H in the diagram below. Verify that the number of paths to H is the sum of the number of paths to F and G.
2. Explicitly compute the number of paths too the points marked C, D, and E in the diagram below. Verify that the number of paths to E is the sum of the number of paths to C and D.
