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Question
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
Solution
A team of 3 boys and 3 girls is to be selected from 5 boys and 4 girls.
3 boys can be selected from 5 boys in `""^5C_3` ways.
3 girls can be selected from 4 girls in `""^4C_3 `ways.
Therefore, by multiplication principle, number of ways in which a team of 3 boys and 3 girls can be selected
= 5C3 x 4C3
= `(5!)/(3!2!) xx (4!)/(3!1!)`
= `(5 xx 4 xx 3!)/(3! xx 2) xx (4 xx 3!)/(3!)`
= 10 x 4 = 40
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