1.3.10 problem 39

There are a total of $\left(\frac{2N}{K}\right)$ possible committees of $K$ people. There are $\left(\frac{N}{j}\right)$ ways to select $j$ couples for the committee. $K-2j$ people need to be selected from the remaining $N-j$ couples such that only one person is selected from a couple. First, we select $K-2j$ couples from the remaining $N-j$ couples. Then, for each of the selected couples, there are $2$ choices for committee membership.