Rework problem 16 from section 2.2 of your text, involving the assignment of tasks to the men and women of a committee. Assume that you have a committee of 11 members, made up of 7 men and 4 women.

Question

In how many ways can the 3 tasks be assigned so that both men and women are given assignments?

Answer 1

So Bryson R.,

WHen you have a complex problem like this, you will find it easiest to break it down into sequential bits. So the two main pieces here are: 1) selection of designees, and 2) assignment of tasks to them.

Do you see why you don't want to try to do these simultaneously? You'd go nuts trying to keep track of your variables!

(1) So -- selection of designees -- this is fairly straightforward -- you need both men and women selected (whyever in the world? Did you need diversity in the group of 8 who aren't assigned tasks?). So you could only choose 1 or 2 women, from your group of 3. (Why not 0 or 3?) From this point on in this part you must treat each of these cases (1 vs. 2 women) separately! Each is a combination. And the selection of the men is also a corresponding combination. Multiply first across the corresponding combinations, THEN add those 2 products. You now have all designee combinations.

(2) Then, you have the 3 tasks, distributed amongst the 3 designees. Assuming you can tell the tasks apart (with committees, one is never completely sure!) that's a permutation. Calculate that, and multiply by the result in part (1) above.

Hope that agrees with whatever you did previously; like Mark M., I'm always a skeptic....

-- Cheers, -- Mr. d.