13 people on the committee: 4 black males, 4 black females,

[Fiona09]

Assume that you have a total of 13 people on the committee: 4 black males, 4 black females, 1 white male, and 4 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?

I have tried several different methods in trying to solve this problem but I really don't have much reason for what I have tried as I do not really know what I am doing. I cannot tell whether or not I use permutations or combinations. I have tried the following approaches:

C(13,3) - C(8,1) * C(8,1)
P(13,3) -P(8,1) - P(8,1)
I have played around with some other numbers but everything comes up wrong.

These problems are really confusing for me. Can someone help?

 

[Fiona09]

I figured it out! The answer is P(13,3) - P(5,3) - P(5,3)

My mistake was working it as a combinations problem instead of using permutations. I didn't realize that order mattered in this problem.