1. ## Combinations

A committee of 7 politicians is chosen from 10 liberal members, 8 labor members and 5 independents. In how many ways can this be done so as to include exactly 1 independent and at least 3 liberal members and at least 1 labor member?

2. What do you think the answer is?
What have you done? Where are you having trouble?

3. I have honestly no idea where to start. Teacher didn't explain how to do these questions.

4. Originally Posted by noobonastick
A committee of 7 politicians is chosen from 10 liberal members, 8 labor members and 5 independents. In how many ways can this be done so as to include exactly 1 independent and at least 3 liberal members and at least 1 labor member?
$\sum\limits_{k = 0}^2 {{\binom{5}{1}}{\binom{8}{k+1}}{\binom{10}{5-k}}}$

5. Sorry, are you sure you havent done anything wrong? My book says the answer is 73 080

6. Originally Posted by noobonastick
Sorry, are you sure you havent done anything wrong? My book says the answer is 73 080
Maybe you need to improve your calculation skills.

7. This is what i calculated.

(5C1).(8C1 + 8C2 + 8C3).(10C5 + 10C4 + 10C3)

8. Originally Posted by noobonastick
This is what i calculated.

(5C1).(8C1 + 8C2 + 8C3).(10C5 + 10C4 + 10C3)
WHY? The answer I gave you is a sum not a product.
$\binom{5}{1}\binom{8}{1}\binom{10}{5}+\binom{5}{1} \binom{8}{2}\binom{10}{4}+\binom{5}{1}\binom{8}{3} \binom{10}{3}$