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Math Help - combinations and permutations

  1. #1
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    combinations and permutations

    There are 5 women and 7 men who are reporters for a magazine. There are 6 articles that need to be written. If 6 reporters are chosen at random to write the articles, what is the probability that 3 are men and 3 are women?

    I got 40,000/117,649. I'm doubting my answer because its such a huge fraction. Please let me know what you guys get and explain!!
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  2. #2
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    Also, how do u do this?

    A family with 5 children is selected at random. What is the probability that the family has atleast 3 boys?
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  3. #3
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    Are you sure this is trigonometry?

    Quote Originally Posted by knicksfan426 View Post

    I got 40,000/117,649. I'm doubting my answer because its such a huge fraction. Please let me know what you guys get and explain!!
    How did you get your answer?

    Quote Originally Posted by knicksfan426 View Post
    There are 5 women and 7 men who are reporters for a magazine. There are 6 articles that need to be written. If 6 reporters are chosen at random to write the articles, what is the probability that 3 are men and 3 are women?
    I was thinking \frac{^7C_3+^5C_3}{^{12}C_6}\approx 0.049
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  4. #4
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    Quote Originally Posted by knicksfan426 View Post
    Also, how do u do this?

    A family with 5 children is selected at random. What is the probability that the family has atleast 3 boys?
    It is assumed the probability of having a boy is equal to the probability of having a girl i.e. 0.5?

    If so use X~ \text{Bi(5,0.5)} and find P(X\geq 3) = P(X=3)+P(X=4)+P(X=5)
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