Question

The number of teams for a mixed doubles tennis match, that can be formed from eight couples, is

• A. $784$
• B. $1820$
• C. $910$
• D. $1568$

Answer 1

The correct option is D $1568$

Mixed doubles tennis match

Each team consists of are man and are woman.

Total ways of selecting are man and woman

from 8 couples $={}^8{C}_1{\times }^8{C}_1$

$=64$

No. of teams for match $=\frac{{}^8{C}_1{\times }^8{C}_1{\times }^7{C}_1{\times }^7{C}_1}{2!}$

$=\frac{3136}{2}=1568$

D is correct