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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?
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Verified Answer
3 boys out of 5 boys can be selected in ${ }^5 C_3$ ways.
3 girls out of 4 girls can be selected in ${ }^4 C_3$ ways.
Number of ways in which 3 boys and 3 girls are selected
$\begin{aligned}
&={ }^5 C_3 \times{ }^4 C_3={ }^5 C_2 \times{ }^4 C_1 \\
&=\frac{5 \times 4}{1 \times 2} \times \frac{4}{1}=40
\end{aligned}$
3 girls out of 4 girls can be selected in ${ }^4 C_3$ ways.
Number of ways in which 3 boys and 3 girls are selected
$\begin{aligned}
&={ }^5 C_3 \times{ }^4 C_3={ }^5 C_2 \times{ }^4 C_1 \\
&=\frac{5 \times 4}{1 \times 2} \times \frac{4}{1}=40
\end{aligned}$
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