Consider a class of 5 girls and 7 boys.

Question:

Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys $A$ and $B$, who refuse to be the members of the same team, is:

1. 200

2. 300

3. 500

4. 350

Correct Option: , 2

Solution:

Required number of ways

$=$ Total number of ways $-$ When $\mathrm{A}$ and $\mathrm{B}$ are always included.

$={ }^{5} \mathrm{C}_{2} \cdot{ }^{7} \mathrm{C}_{3}-{ }^{5} \mathrm{C}_{1}^{5} \mathrm{C}_{2}=300$