A committee of four congressmen will be selected from a group 7 democrats and 3 republicans. find the number of different committees containing A).exactly one democrat B).exactly three democrats
When answering "how many combinations" problems, we imagine we are placing the items (people in this case) into positions. To get the answer, we then multiply the possible ways to place weach position. So... A) Exactly one democrat: Since we need exactly 1 democrat, there are 7 possible people to choose from. Now because the committee is to have 4 people, and we have 1 democrat, the remaining 3 people would be republicans. There is only one way to pick those 3 republicans since that's all there is. So, we have 7 ways to pick the democrat and 1 way to pick the republicans, giving us 7\times1=7
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