Question 1111234: Suppose that a class contains 15 boys and 30 girls, and that 10 students are to be selected at random for a special assignment. Find the probability that exactly 3 boys will be selected.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! There are 45 students and we select 10 students from that group
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There are 45C10 ways to do that selection process, where nCr = n! / (r! * (n-r)!)
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Therefore,
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45C10 = 45! / (10! * (45-10)!) = 3,190,187,286 ways
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We want to find the number of ways we can choose 3 boys from the 15 boys
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15C3 = 15! / (3! * (15-3)!) = 455 ways to choose 3 boys from the 15 boys
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Now, exactly 3 boys implies that there are exactly 7 girls in the group of 10 selected
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There are 30C7 = 30! / (7! * (30-7)!) = 2,035,800 ways to choose the 7 girls
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Probability that exactly 3 boys will be selected = (455*2035800)/3190187286 = 0.29035568
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