Given a bag contains $5$ black and $6$ red balls

Number of ways we can select $2$ black balls from $5$ black balls are

\[\Rightarrow {{~}^{5}}{{C}_{2}}=\]

Number of ways we can select $3$ red balls from $6$ red balls are

\[\Rightarrow {{~}^{6}}{{C}_{3}}=\]

Number of ways $2$ black and $3$ red balls can be selected are

\[^{5}{{C}_{2}}~\times {{~}^{6}}{{C}_{3}}\]

∴ Number of ways in which $2$ black and $3$ red balls can be selected from $5$ black and $6$ red balls are $200$