Question

4 couples (husband-wife) attend a party. In how mpny ways can 2 persons be selected from these 8 persons such that,

(i) two persons selected are husband and wife?
(ii) one is a male and the other is a female?
(iii) one is a male and the other Is a female but they are not husband and wife?

Answer 1

4 couples are there. 2 persons are selected from 8 persons.

(i) Two persons selected are husband and wife:
If selected two persons are husband and wife. then they are one couple of 4 couples.
∴ Total combinations = ⁴C₁ = 4

(iii) One Is a male and the other is a female:
In 8 persons, 4 are males and 4 are females.
One male can be selected in ⁴C₁ ways andone female can be selected In ⁴C₁ ways.
∴ Total combinatíons = ⁴C₁ × ⁴C₁ = 4 × 4 = 16

(iii) One is a male and the other is a female but they are not husband and wife:
Total combinations
[Total combinations in which one is a male and one is female – Total combinations in which they are husband and wife]
= 16 – 4 = 12