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Math Help - Probablity Question? Choosing bills?

  1. #1
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    Probablity Question? Choosing bills?

    Out of 10 $20 bills, 2 are counterfeit, 6 bills are chosen at random. What is the probability that both counterfeit bills are chosen?

    --my attempt--

    C(10,6)/(C(6,2) *C(10,2))

    Is this correct? I am not sure.

    Thanks
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  2. #2
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    Re: Probablity Question? Choosing bills?

    Quote Originally Posted by blackZ View Post
    Out of 10 $20 bills, 2 are counterfeit, 6 bills are chosen at random. What is the probability that both counterfeit bills are chosen?
    Your notion is off base.
    Standard notation is \binom{n}{k}=\frac{n!}{k!(n-k)!}, n things choosing k.

    So the answer will be \frac{\dbinom{8}{4}}{\dbinom{10}{6}}.
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  3. #3
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    Re: Probablity Question? Choosing bills?

    Hello, blackZ!

    Out of ten $20 bills, two are counterfeit.
    Six bills are chosen at random.
    What is the probability that both counterfeit bills are chosen?

    There are: _{10}C_6 \:=\:210 possible outcomes.

    There are: 2 fake and 8 real bills.
    We want: 2 fake and 4 real bills.

    There are: . (_2C_2)(_8C_4) \:=\:1\cdot70 \:=\:70 ways.


    P(\text{2 fake, 4 real}) \:=\:\frac{70}{210} \:=\:\frac{1}{3}

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