A committee of four people, containing at least one man and one woman, must be chosen from four men and three women. A committee of four people, containing at least one man and one woman, must be chosen from four men and three women. How many different committees are possible?

I dont really now how to solve this. I tried solve them by counting them in groups. but thats not really the right way I guess. Can anyone give me a clue to solve this.
Hint: Choose four people from seven.  You only need to avoid the one combination of picking all four men.
Let's think about this. There are four ways to choose one man and three ways to choose one woman. This means that there are 4 * 3 = 12 ways to choose one man and one woman. So what's left over? We have 3 men + 2 woman left to fill the remaining two positions. Gender doesn't matter anymore since we've met the criteria of picking one man and one woman. That means there are 5 * 4 = 20 ways to choose the rest of the committee. Combining what we now know, there are 12 * 20 = 240 ways to organize this committee.