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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?
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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
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