Question

Six married couples are sitting in a room. The number of ways in which four persons can be selected, such that there is exactly one married couple among the four, is

• A. 276
• B. 600
• C. 840
• D. 240

Answer 1

Answer: (D)

Select one couple in ${ }^{6} C_{1}$ ways.
Remaining $5$ couples have $5$ men and $5$ women.
Select two men or two women or one man and one women so that they are not couple. Two men can be selected in ${ }^{5} C_{2}$ ways Two women can be selected in ${ }^{5} C_{2}$ ways One man and one woman such that they are not a couple can be selected in ${ }^{5} C_{1} \times{ }^{4} C_{1}$ ways
Hence, the total number of ways $={ }^{6} C_{1}$
${ }^{5} C_{2}+{ }^{5} C_{2}+{ }^{5} C_{1}{ }^{4} C_{1}=610+10+20=240$