14. $n$ couples are arbitrarily arranged in a row, find the total number of arrangements where no couple is adjacent.
14. Let $S$ denote the set of all different permutations of $n$ couples, and $A_{i}$ denote the set of permutations where the $i$-th couple is adjacent. Then, by the principle of inclusion-exclusion, the total number of permutations sought is $\left|\bar{A}_{1} \cap \bar{A}_{2} \cap \cdots \cap \bar{A}_{n}\right|=(2 n)!-C_{n}^{1} \cdot 2(2 n-1)!+$ $C_{n}^{2} \cdot 2^{2} \cdot(2 n-2)!-\cdots+(-1)^{k} C_{n}^{k} 2^{k}(2 n-k)!+\cdots+(-1)^{n} C_{n}^{n} \cdot 2^{n} \cdot n!$