In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?

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Solution

There are 5 boys and 4 girls. We have to select 3 out of 5 boys and 3 out of 4 girls.

$∴$ Number of ways of selection

= $^{5} C_{3} \times^{4} C_{3}$

= $\frac{5!}{3! 2!} \times \frac{4!}{3! 1!} = 10 \times 4 = 40.$

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In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?

There are 5 boys and 4 girls. We have to select 3 out of 5 boys and 3 out of 4 girls. ∴ Number of ways of selection = 5C3×4C3 = 5!3! 2!×4!3! 1!=10×4=40.

There are 5 boys and 4 girls. We have to select 3 out of 5 boys and 3 out of 4 girls.

$∴$ Number of ways of selection

= $^{5} C_{3} \times^{4} C_{3}$

= $\frac{5!}{3! 2!} \times \frac{4!}{3! 1!} = 10 \times 4 = 40.$