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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.

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  • $\begingroup$ Are the people considered different, or do we only look at "how many there are of men and women"? $\endgroup$ – Matti P. Nov 1 '19 at 11:10
  • $\begingroup$ Hint: give names to the men and think about how you would count concretely the committees. $\endgroup$ – Gribouillis Nov 1 '19 at 11:28
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Hint: Choose four people from seven. You only need to avoid the one combination of picking all four men.

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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.

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