Question

In how many ways can a mixed double tennis game be arranged from $7$ married couples. If no husband and wife play in the same game?

• A. $28$
• B. $70$
• C. $210$
• D. $420$

Answer 1

The correct option is D $420$

$420$

2 men selected from 7 men ${=}^7{C}_2$ ways

2 women out of remaining 5 are chosen in ${}^5{C}_2$ ways

The required number of arrangements,

${=}^7{C}_2{\times }^5{C}_2\times 2$

$=420$