SOLUTION: I need your help with my homework. A group of 10 peopleincludes one married couple. If 4 people are sellected ar random, what is the probability that the married couple is selec

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Question 247651: I need your help with my homework.
A group of 10 peopleincludes one married couple. If 4 people are sellected ar random, what is the probability that the married couple is selected?
Thank very much.
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
There are 10 people, so there are 10 ways you could pick the first person. Those are the possibilities. Two of them are married, so the chance that you pick either one of the married couple is 2/10 = 1/5 or 20%.
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Now that you have picked one member of the married couple, there are 9 ways you can pick the next person. But only 1 of those is the spouse. So the probability is 1/9.
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So the chance you pick the couple = 1/5 * 1/9 = 1/45
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As a check, you can determine the number of combinations of 2 people from a set of 10. That defines the number of possibilities.
10%21%2F%282%21%2A8%21%29
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%2810%2A9%2A8%21%29%2F%282%21+%2A+8%21%29
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The 8! terms cancel. So we have %2810%2A9%29%2F2+=+45. There is only 1 way you pick the couple. 1/45.
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