A team consists of 6 boys and 4 girls and another team consists of 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.

First team consist of  6 boys and 4 girls, second team consist of 5 boys and 3 girls.

match will be between b-b and g-g

from team 1, selection of one boy will be 6C1

from team 2 selection of one boy will be 5C1

so number of matches between boys will be 6C1×5C1=30

and similarly for girls , the number of matches will be 4C1×3C1=12

so the total number of matches will be 12 + 30 = 42