Question: Executives from 25 student clubs, one male and one female each, are attending a workshop on student violence. How many ways can a committee be set up of 5 men and 7 women if only one male or female from each club can be selected?
I'm currently taking a Grade 12 Data Management course, and this is a question I have from an assignment. I'm supposed to answer it using permutations and combinations preferably. I have tried answering it by doing $(12C5)(12C7)$ and got the answer of 627,264. However, I am not sure if this is the correct method, or if my answer is right. Thanks so much in advance for any help you can give!
I would say $${25\choose 5}\cdot{20\choose 7}$$
First you take 5 man from 25 clubs, and then from the rest of 20 clubs you take 7 woman.