In how many ways can a team of $3$ boys and $3$ girls be selected from $5$ boys and $4$ girls?
In how many ways can a team of $3$ boys and $3$ girls be selected from $5$ boys and $4$ girls?
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 $^{5} C_{3}$ ways.
$3$ girls can be selected from $4$ girls in $^{4} C_{3}$ ways.
Therefore, by multiplication principle, number of ways in which a team of $3$ boys and $3$ girls can be selected $=^{5} C_{3} \times^{4} C_{3}=\frac{5 !}{3 ! 2 !} \times \frac{4 !}{3 ! 1 !}$
$=\frac{5 \times 4 \times 3 !}{3 ! \times 2} \times \frac{4 \times 3 !}{3 !}$
$=10 \times 4=40$
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- [JEE MAIN 2023]