A team consists of 6 boys and 4 girls, and other has 5 boys and 3 girls. How many single matches can be arranged between the two teams when a boy plays against a boy, and a girl plays against a girl?
Given: Singles matches are to be played, either a boy plays against a boy, and a girl plays against a girl.
A number of ways to select a boy from team 1 is 6C1. Similarly, Number of ways to select a boy from team 2 is 5C1
Hence number of singles matches between boys is 6C1 × 5C1 = 6 × 5 = 30
A number of ways to select a girl from team 1 is 4C1. Similarly, Number of ways to select a girl from team 2 is 3C1
Hence number of singles matches between girls is 3C1 × 4C1 = 4 × 3 = 12
The total number of matches = 30 + 12 = 42.