From a class of 14 boys and 10 girls, 10 students are to be chosen for a

2 girls who won the prize last year are surely to be taken. So, we have to make a selection of 8 students out of 14 boys and 8 girls, choosing at least 4 boys and at least 2 girls.

Thus, we may choose:

(4 boys, 4 girls) or ( 5 boys, 3 girls) or ( 6 boys, 2 girls)

Therefore, the required number of ways $=\left({ }^{14} \mathrm{C}_{4} \times{ }^{8} \mathrm{C} 4\right)+\left({ }^{14} \mathrm{C}_{5} \times{ }^{8} \mathrm{C}_{3}\right)+\left({ }^{14} \mathrm{C}_{6} \times{ }^{8} \mathrm{C}_{2}\right)$