Problem 11.6. Given the set of numbers $\{-1,-2,-3, \ldots,-26\}$. On the board, all possible subsets of this set were written, each containing at least 2 numbers. For each written subset, the product of all numbers belonging to that subset was calculated. What is the sum of all these products?
Answer: 350.

Solution. Consider the expression $(1-1)(1-2)(1-3) \ldots(1-26)$, the value of which is 0. Expand this expression without combining like terms, resulting in the sum $1^{26}-1^{25}(1+2+3+\ldots+26)+S$. Notice that the sum $S$ coincides with the sum from the problem's condition. Therefore, it equals $0-1+(1+2+3+\ldots+26)=350$.