The number of ways in which 2 black balls out of 5 black balls are selected $={ }^5 \mathrm{C}_2$
The number of ways in which 3 red balls out of 6 red balls are selected $={ }^6 \mathrm{C}_3$
The number of ways in which 2 black and 3 red balls can be selected $={ }^5 \mathrm{C}_2 \times{ }^6 \mathrm{C}_3$
$=\frac{5 \times 4}{1 \times 2} \times \frac{6 \times 5 \times 4}{1 \times 2 \times 3}=10 \times 20=200$