Thirty six identical chairs must be arranged in rows with the same number of chairs in each row. Each row must contain at least three chairs, and there must be at least three rows. A row 1S parallel to the front of the room. How many different arrangements are possible?

Case 1: When there is 3 chairs in each row, then total rows = $$\frac{36}{3} = 12$$ (Valid)

Case 2: When there is 4 chairs in each row, then total rows = $$\frac{36}{4} = 9$$ (Valid)

Case 3: When there is 6 chairs in each row, then total rows = $$\frac{36}{6} = 6$$ (Valid)

Case 4: When there is 9 chairs in each row, then total rows = $$\frac{36}{9} = 4$$ (Valid)

Case 5: When there is 12 chairs in each row, then total rows = $$\frac{36}{12} = 3$$ (Valid)

Hence, total possible arrangements = 5