Question

In how many ways can a lawn tennis mixed double be made tip from seven married couples if no husband and wife play in the same set?

Answer 1

Let two husbands A, B be selected out of seven males in = $7_{C_2}$ ways, excluding their wives, we have to select two ladies C, D out of remaining 5 wives is = $5_{C_2}$ ways. Thus, number of ways of selecting the players for mixed double is = $7_{C_2}\times 5_{C_2}=21\times 10=210$ Now, suppose A chooses C as partner (B will automatically go to D) or A chooses D as partner (B will automatically go to C) Thus we have, 4 other ways for teams. Required number of ways = $210\times 4=840$