Question

The number of ways in which a mixed doubles game in tennis can be arranged from 5 married couples, if no husband and wife play in the same game, is

• A. 46
• B. 54
• C. 60
• D. None of these

Answer 1

Answer: (C)

60

Answer 2

Let the sides of the game be A and B. Given 5 married couples, i.e., 5 husbands and 5 wives. Now, 2 husbands for two sides A and B can be selected out of $5 = ^5C_2 = 10$ ways. After choosing the two husbands their wives are to be excluded (since no husband and wife play in the same game). So we have to choose 2 wives out of remaining $5 - 2 = 3$ wives i.e., $^3C_2 = 3$ ways. Again two wives can interchange their sides A and B in $2! = 2$ ways. By the principle of multiplication, the required number of ways $= 10 ? 3 ? 2 = 60$