Six married couples are sitting in a room. The number of ways in which four persons can be selected, such that there is exactly one married couple among the four, is

Step-by-step solution

Select one couple in C 6 1 ways. Remaining 5 couples have 5 men and 5 women. Select two men or two women or one man and one women so that they are not couple. Two men can be selected in C 2 5 ways Two women can be selected in C 2 5 ways One man and one woman such that they are not a couple can be selected in C 1 5 × C 1 4 ways Hence, the total number of ways = C 6 1 C 5 2 + C 5 2 + C 5 1 C 4 1 = 6 10 + 10 + 20 = 240