Question

6 married couples are present in a room. If 4 people are chosen at random, then the chance that exactly one married couple is among the 4 is?

• A. 8/33
• B. 16/66
• C. 16/33
• D. 23/33

Answer 1

The correct option is C

16/33

Total sample space: ${}^{12}{C}_4$ =495

For selecting one married couple: ${}^6{C}_1\times 10\times \frac{8}{2}=6\times 10\times 4=240$

$P\left(E\right)=\frac{240}{{}^{12}{C}_4}=\frac{16}{33}$.