Counting

To find the number of paths from A to I, if each step must be in a right-ward direction, we can use the principle of multiplication. 

Starting from A, we have only one option to move to C. From C, we can move to either D or E. From D, we can only move to E, and from E, we can move to either F or G. From F, we can only move to G, and from G, we can move to either H or I. Finally, from H, we can only move to I.

Therefore, the total number of paths from A to I, moving only in a right-ward direction, is the product of the number of choices at each step:

1 (choice at A) x 2 (choices at C) x 1 (choice at D) x 2 (choices at E) x 1 (choice at F) x 2 (choices at G) x 1 (choice at H) = 4

So there are 4 possible paths from A to I, if each step must be in a right-ward direction.