Question

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?

Answer 1

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

Answer 2

I'm getting 250. I'm not entirely sure about this answer however. Can someone verify?

Answer 3

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.

Answer 4

ill check

Answer 5

it says incorrect

Answer 6

Do you have a limited number of tries?

Answer 7

no

Answer 8

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.

Answer 9

505 is what it results in

Answer 10

incorrect

Answer 11

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.

Answer 12

that did not work

Answer 13

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

Answer 14

well i have to give up
i am leaving 4 unanswered

Answer 15

I cant see the screen

Answer 16

or the paer

Answer 17

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

Answer 18

sorry just 3

Answer 19

3 problems

Answer 20

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

Answer 21

I have thank you so much for everything

Answer 22

**Bookmark**