Q. 123

# 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?

Answer :

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 ^{6}C_{1}. Similarly, Number of ways to select a boy from team 2 is ^{5}C_{1}

Hence number of singles matches between boys is ^{6}C_{1} × ^{5}C_{1} = 6 × 5 = 30

A number of ways to select a girl from team 1 is ^{4}C_{1}. Similarly, Number of ways to select a girl from team 2 is ^{3}C_{1}

Hence number of singles matches between girls is ^{3}C_{1} × ^{4}C_{1} = 4 × 3 = 12

The total number of matches = 30 + 12 = 42.

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Which of the following are true :

(2 + 3)! = 2! + 3!

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