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NCERT Class XI Mathematics - Permutations and Combinations - Solutions

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Question : 25 of 41
Marks: +1, -0
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
Solution:  
3 boys can be selected from 5 boys in  5C3\,{}^{5}C_{3} ways & 3 girls can be selected from 4 girls in  4C3\,{}^{4}C_{3} ways.
∴ Required number of ways of team selection
=  5C3\,{}^{5}C_{3} ×  4C3\,{}^{4}C_{3} = 5!2!3!×4!3!1!\frac{5!}{2!3!} \times \frac{4!}{3!1!} = 5×42\frac{5\times 4}{2} × 4 = 40
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