Question

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

Answer 1

We have
Number of girls $=4$
Number of boys $=5$
$\therefore 3$ girls out of $4$ girls can be selected in ${}^4{C}_3$ ways and $3$ boys out of $5$ boys can be selected in ${}^5{C}_3$ ways.
$\therefore$ Required number of ways
${}^5{C}_3{\times }^4{C}_3$
$=\frac{5\times 4\times 3}{3\times 2\times 1}\times \frac{4\times 3\times 2}{3\times 2\times 1}$
$=10\times 4=40$