Question

There are $3$ white and $5$ red roses in a basket. In how many ways can $4$ flowers be removed from the basket so that they contain $2$ red flowers?

Answer 1

There are $5$ red flowers. The number of ways in which $2$ flowers can be removed from $5$ red flowers is ${{}^{5}C}_2$.
Then remaining $2$ flowers from $3$ white flowers in ${{}^{3}C}_2$ ways
$\therefore$ total number of ways
$={{}^{5}C}_2\times {{}^{3}C}_2$
$=\frac{5\times 4}{2\times 1}\times \frac{3\times 2}{2\times 1}$
$=10\times 3$

$=30$