# 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? - Mathematics

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.
∴ 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.
∴ Number of ways of arranging a match between the girls of the two teams = 4$\times$3= 12

∴ Total number of matches = 30 + 12 = 42

Concept: Combination
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 16 Permutations
Exercise 16.2 | Q 12 | Page 15