Question -
Answer -
Given:
A team consists of 6boys and 4 girls, and other team has 5 boys and 3 girls.
Let team 1 be = 6 boysand 4 girls
Team 2 be = 5 boys and3 girls
Singles matches are tobe played, either a boy plays against a boy, and a girl plays against a girl.
So, number ofways to select a boy from team 1 is 6C1. Similarly,Number of ways to select a boy from team 2 is 5C1
Hence number ofsingles matches between boys is 6C1 × 5C1 =6 × 5 = 30
A number of waysto select a girl from team 1 is 4C1. Similarly,Number of ways to select a girl from team 2 is 3C1
Hence number ofsingles matches between girls is 3C1 × 4C1 =4 × 3 = 12
∴ The total number ofsingle matches are = 30 + 12 = 42