6 Let the arithmetic mean of all elements in the set $A=\left\{a_{1}, a_{2}, \cdots, a_{n}\right\}$ be denoted as $P(A)\left(P(A)=\frac{a_{1}+a_{2}+\cdots+a_{n}}{n}\right)$. If $B$ is a non-empty subset of $A$ and $P(B)=P(A)$, then $B$ is called a “balanced subset” of $A$. Try to find the number of all “balanced subsets” of the set $M=\{1,2,3,4,5,6,7,8,9\}$. (Provided by Tao Pingsheng)