## Pulsified333 one year ago Assume that you have a total of 12 people on the committee: 3 black males, 3 black females, 1 white male, and 5 white females. Party rules require that at least one black and at least one female hold one of the three offices. Note that if individuals change offices, then a different selection exists. In how many ways can the officers be chosen while still conforming to party rules?

1. rock_mit182

DO you have any options ?

2. rock_mit182

restriction number , at least 1 black: C(12,6) where 12 is the total of people and 6 is the same as say 3 black men or 3 black female: $C (12,6) = \frac{ 12! }{ (12-6)! *6! }$

3. rock_mit182

@Pulsified333 are you following ?

4. Pulsified333

yes thank you very much

5. rock_mit182

wait that is not the whole answer

6. rock_mit182

we're missing the second part

7. Pulsified333

8. rock_mit182

how did you do it ?

9. Pulsified333

P(12,3)-P(6,3)-P(4,3)