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Math Help - Probability Question Check

  1. #1
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    Probability Question Check

    Hi,

    15 phones have just been received at an authorized service center. 5 are cellular, 5 are cordless, and 5 are corded. Suppose service tickets have been issued for these phones allocating all numbers 1 through 15 indicating the order in which they will be serviced. Find the probabilities that:

    after having repaired 10 phones, there are phones of exactly two of the three types remaining to be serviced.

    I computed the answer to be [3 x [(10 C 5) - 2]]/(15 C 10)

    Is this correct
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  2. #2
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    Quote Originally Posted by shogunhd View Post
    Hi,

    15 phones have just been received at an authorized service center. 5 are cellular, 5 are cordless, and 5 are corded. Suppose service tickets have been issued for these phones allocating all numbers 1 through 15 indicating the order in which they will be serviced. Find the probabilities that:

    after having repaired 10 phones, there are phones of exactly two of the three types remaining to be serviced.

    I computed the answer to be [3 x [(10 C 5) - 2]]/(15 C 10)

    Is this correct
    I get the same answer that you do

    (but used a different approach. My numerator is:

    3\left[ {5 \choose 4} \cdot {5 \choose 1} + {5 \choose 3} \cdot {5 \choose 2} + {5 \choose 2} \cdot {5 \choose 3} + {5 \choose 1} \cdot {5 \choose 4}\right]


    = 3\left[ 2 \left\{ {5 \choose 4} \cdot {5 \choose 1} + {5 \choose 3} \cdot {5 \choose 2} \right \} \right]


    = 6 \left \{ {5 \choose 4} \cdot {5 \choose 1} + {5 \choose 3} \cdot {5 \choose 2} \right \} = 6 (5^2 + 10^2) = 750 )
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