Question:
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?
Solution:
A boy can be selected from the first team in 6 ways and from the second team in 5 ways.
$\therefore$ Number of ways of arranging a match between the boys of the two teams $=6 \times 5=30$
Similarly, A girl can be selected from the first team in 4 ways and from the second team in 3 ways.
$\therefore$ Number of ways of arranging a match between the girls of the two teams $=4 \times 3=12$
$\therefore$ Total number of matches $=30+12=42$