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?

For no married couples: choose 4 from the 8 available couples, considering that within each couple, we can have either one of the two partners.
$\binom{8}{4} \times 2^4$
Now divide this by the total number of selections we can make from 16 people:
$$\frac{\binom{8}{4} \times 2^4}{\binom{16}{4}} = \frac{8}{13} \approx 0.6154 $$
