Consider a class of 5 girls and 7 boys. The number of different...

\left$$\begin{array}{ll}7B \\ 5G\end{array}$$\right\} \to\left($$\begin{array}{ll}3B \\ 2G\end{array}$$\right)

Total number of ways of forming a team of $3$ boys and $2$ girls $= {}^{7}{C}_{3} \times {}^{5}{C}_{2} =$\dfrac{7.6 . 5}{1.2 . 3} \times \dfrac{5.4}{1.2} =$350$

Total number of ways of forming a team if two specific boys ${B}_{1}, {B}_{2}$ always join the team

$= {}^{5}{C}_{1} \times {}^{5}{C}_{2} = 50

So, the total number of ways of forming a team so that two specific boys never come together

= 350 - 50 = 300