Number of ways in which a lawn-tennis mixed double be made from seven married couples if no husband and wife play in the same set is 

We first select 2 men out of 7 in ${ }^7{C}_2$ ways. Now we exclude the wives of these two selected men and so select2ladies from remaining 5 ladies in ${ }^5{C}_2$ ways. Let A, B be two men and X, Y be the ladies playing in one set. Then we can have

(i) A and X plying against B and Y. 

(ii) A and Y playing against B and X.

Then the total number of ways is ${ }^7{\mathrm{C}}_2{\times }^5{\mathrm{C}}_2\times 2=21\times 10\times 2=420$