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 $={}^6{C}_1$
${}^5{C}_2+{}^5{C}_2+{}^5{C}_1{}^4{C}_1=610+10+20=240$