Question 33
Let the set $X = \{1,2,...,8\}$ and two nonempty disjoint subsets $A, B$ of $X$ with union the set $X$. Let $P_A$ be the product of the elements of the set $A$ and $P_B$ be the product of the elements of the set $B$. Determine the least possible value of the sum $P_A + P_B$.