Mathematics - Permutation & Combination Question with Solution | TestHub

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

Total number of ways of forming a team of$3$boys and$2$girls$={}^7{C}_3\times {}^5{C}_2=\frac{7.6.5}{1.2.3}\times \frac{5.4}{1.2}=350$

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

$=350-50=300$