There are ten boys $B_1,B_2,\dots .,B_{10}$ and five girls $G_1$, ${\mathrm{G}}_2,\dots .{\mathrm{G}}_5$ in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both $B_1$ and $B_2$ together should not be the members of a group, is

n(B)=10,n(G)=5 The number of ways of forming a group of  3 boys and$\begin{array}{l}3 \mathrm{girls}{=}^{10}{\mathrm{C}}_3{\times }^5{\mathrm{C}}_3\\ =\frac{10\times 9\times 8}{3\times 2}\times \frac{5\times 4}{2}=1200\end{array}$ 

The number  of ways in which   two particular boys $B_1 and B_2$ be the members of the group together$={ }^8{C}_1\times { }^5{C}_3=8\times 10=80$

The number  of ways in which   two particular boys $B_1 and B_2$ are not in  the same group together=1200-80=1120