Step 1: Identify fat-soluble vitamins.
Fat-soluble vitamins are A, D, E, K. From the list: A, D, K (3 vitamins).
Step 2: Identify water-soluble vitamins.
Water-soluble vitamins are B vitamins and C. From the list: C, B$_1$, B$_6$ (3 vitamins).
Step 3: Determine the number of fat-soluble and water-soluble vitamins respectively.
Number of fat-soluble vitamins = 3
Number of water-soluble vitamins = 3
Thus, the answer is $ \boxed{3, 3} $.
In the Haworth structure of the following carbohydrate, various carbon atoms have been numbered. The anomeric carbon is numbered as: