## anonymous 4 years ago FINAL ONE!!!! THANKS TO ALL THOSE EXPLAINING THESE PROBLEMS FOR ME!!!!! Assume that you have a total of 14 people on the committee: 2 black males, 5 black females, 2 white males, and 5 white females. Party rules require that at least one black and at least one female hold one of the three offices. In how many ways can the officers be chosen while still conforming to party rules?

1. ash2326

Give me some time, I'm trying to solve this. :)

2. KingGeorge

3. KingGeorge

Gotten by the formula $\left( \begin{matrix} 5 \\ 1 \end{matrix}\right) \cdot \left( \begin{matrix} 9 \\ 2 \end{matrix}\right) + \left( \begin{matrix} 2 \\ 1 \end{matrix}\right) \cdot \left( \begin{matrix} 5 \\ 1 \end{matrix}\right) \cdot \left( \begin{matrix} 7 \\ 1 \end{matrix}\right)$However, I'm pretty sure there are committees I've counted at least twice.

4. anonymous

ill check

5. anonymous

it says incorrect

6. KingGeorge

Do you have a limited number of tries?

7. anonymous

no

8. KingGeorge

Next possibility I have is$5\cdot \left( \begin{matrix} 11 \\ 2 \end{matrix}\right) + 2\cdot 10 \cdot 11 +10$This was obtained by breaking down into three case. Case 1: 0 black males. Case 2: 1 black male. Case 3: 2 black males.

9. KingGeorge

505 is what it results in

10. anonymous

incorrect

11. barrycarter

Total number of committees ignoring rules: C(14,3) or 364 Committees with just males: C(4,3) or 4 Committees with just whites: C(7,3) or 35 Committees with just white males: 0 (there are only 2 white males). So the total is 364-4-35 or 325.

12. anonymous

that did not work

13. ash2326

Let's find the total no. of ways of alloting= 14 C3=364 now we'll subtract the following cases from total no. of ways commitee with whites= 7C3=35 commitee with males= 4C3=4 total =39 Our required =364-39=325 ways

14. anonymous

well i have to give up i am leaving 4 unanswered

15. anonymous

I cant see the screen

16. anonymous

or the paer

17. Directrix

Givng up is not an option. Are you talking about problem #4 or 4 unworked problems?

18. anonymous

sorry just 3

19. anonymous

3 problems

20. anonymous

they all are posted on here we have left two unanswered completely then some partials can you view them through my profile?

21. anonymous

I have thank you so much for everything

22. anonymous

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