What is the probability that no married couples are among the chosen? Eight married couples are standing in a room. 4 people are randomly chosen. What is the probability that no married couples are among the chosen?

Another way to figure this out would be to choose 4 different married couples to provide a chosen person (there are $\left(\begin{array}{c} 8\\\ 4\end{array}\right)=70$ ways to do this). Then pick one member of each of the 4 chosen couples (there are $2^4=16$ ways to do this). So altogther there are $70\cdot 16=1120$ ways to choose 4 people so that no two are married to each other.

So the probability of none married to each other among the 4 chosen is $\frac{1120}{\left(\begin{array}{c} 16\\\ 4\end{array}\right)}=\frac{1120}{1820}=\frac8{13}$.

So same as John's answer, just a different approach to counting in the problem.