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 members of the same team, is:

Accepted Answer

Choose 2 girls: $\binom52=10$ ways (common factor).

For the 3 boys with A, B not both included:
- Include A, exclude B: choose 2 more from remaining 5: $\binom52=10$
- Include B, exclude A: $\binom52=10$
- Include neither A nor B: choose 3 from remaining 5: $\binom53=10$

$$\text{Total} = 10\times(10+10+10) = 300$$

Solutions · 1