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 g…

Group -A Group -B

4B + 1G OB + 3G
3B + 2G 1B + 2G
2B + 3G 2B + 1G

\(Totalpossiblecases\\ ={}^{7}\mathrm{C}_{4}\times {}^{3}\mathrm{C}_{1}\times {}^{6}\mathrm{C}_{0}\times {}^{5}\mathrm{C}_{3}+{}^{7}\mathrm{C}_{3}\times {}^{3}\mathrm{C}_{2}\times {}^{6}\mathrm{C}_{1}\\ \times {}^{5}\mathrm{C}_{2}+{}^{7}\mathrm{C}_{2}\times {}^{3}\mathrm{C}_{3}\times {}^{6}\mathrm{C}_{2}\times {}^{5}\mathrm{C}_{1}\\ =\frac{7\times 6\times 5}{3\times 2}\times 3\times 1\times \frac{5\times 4}{2}+\frac{7\times 6\times 5}{3\times 2}\\ \times 3\times 6\times \frac{5\times 4}{2}+\frac{7\times 6}{2}\times 1\times \frac{6\times 5}{2}\times 5\\ =1050+6300+1575\\ =8925\)