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Counting Problem (ways of choosing 3 with conditions)

  1. Feb 11, 2016 #1
    1. The problem statement, all variables and given/known data
    Given 9 good light bulbs and 4 defective light bulbs, how many ways can you select 3 such that you get exactly 1 defective bulb?

    2. Relevant equations
    C(n,r)

    3. The attempt at a solution
    I understand total ways to select is C(13,3)=286, and that total ways to select only good bulbs is C(9,3)=84. Subtracting these would give 202 ways to get 1 or more defective bulb. Not sure how to further differentiate these cases...answer provided is 144.

    If I just use rule of counting, I can pick from 4 bad, 9 good, then 8 bad in any order which is 288...double the provided answer.
     
  2. jcsd
  3. Feb 11, 2016 #2

    Samy_A

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    In how many ways can you select 1 defective bulb?
    In how many ways can you select 2 good bulbs?
     
  4. Feb 11, 2016 #3
    C(4,1)*C(9,2). Thank you.
     
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