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?

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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?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Give me some time, I'm trying to solve this. :)
I'm getting 250. I'm not entirely sure about this answer however. Can someone verify?
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.

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Other answers:

ill check
it says incorrect
Do you have a limited number of tries?
no
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.
505 is what it results in
incorrect
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.
that did not work
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
well i have to give up i am leaving 4 unanswered
I cant see the screen
or the paer
Givng up is not an option. Are you talking about problem #4 or 4 unworked problems?
sorry just 3
3 problems
they all are posted on here we have left two unanswered completely then some partials can you view them through my profile?
I have thank you so much for everything
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