Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls.

Question

Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group $A$ and the remaining 3 from group $B$, is equal to :

Accepted Answer

$$\[\begin{gathered} \text { C-I } \quad  (3 \mathrm{G} \quad  2 \mathrm{~B}) \quad (1 \mathrm{G} \quad  2 \mathrm{~B}) \ \text { C-II } \quad  (2 \mathrm{G} \quad  3 \mathrm{~B}) \quad (2 \mathrm{G} \quad  1 \mathrm{~B}) \ \text { C-III } \quad  (1 \mathrm{G} \quad  4 \mathrm{~B}) \quad (3 \mathrm{G} \quad  0 \mathrm{~B}) \end{gathered}$$\]

$$\begin{aligned}
& \text { Total }=\text { C-I }+ \text { C-II }+ \text { C-III } \
& ={ }^7 \mathrm{C}_2 \cdot{ }^3 \mathrm{C}_3 \cdot{ }^6 \mathrm{C}_2 \cdot{ }^5 \mathrm{C}_1+{ }^7 \mathrm{C}_3 \cdot{ }^3 \mathrm{C}_2 \cdot{ }^6 \mathrm{C}_1{ }^5 \mathrm{C}_2+{ }^7 \mathrm{C}_4 \cdot{ }^3 \mathrm{C}_1 \cdot{ }^6 \mathrm{C}_0 \cdot{ }^5 \mathrm{C}_3 \
& =8925
\end{aligned}$$

Solutions · 1