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I am a little confused at how to solve the Permutations

  1. Jan 26, 2007 #1
    I am a little confused at how to solve the following problem:

    In how many ways can five distinct Martians, ten distinct Vesuvians, and eight distinct Jovians wait in line if no two Martians stand together?

    What is throwing me off is the addition of another group - if it was just Martians and Vesuvians it would be easy. My guess is P(10,5) = (10*9*8*7*6)

    Am I correct or did I mess this up?
  2. jcsd
  3. Jan 26, 2007 #2
    It doesn't matter how the Vesuvians and Jovians stand so thinking of these as ALIENS you DO have two groups 5 Martians and 18 ALIENS
  4. Jan 26, 2007 #3
    So my calculation was wrong? It should be P(18,5) ?
  5. Jan 26, 2007 #4
    How many ways could you arrange the ALIENS? Remember they are all distinct.

    How many ways could you then slot in the Martians to meet the conditions?
  6. Jan 26, 2007 #5
    Right - Because there are 18 Vesuvians and Jovians, the Martians can either fit in the front of the line, middle or end of the line. In which case there would be 19 spots where they could fit in line. P(19,5) = 1,395,360
  7. Jan 26, 2007 #6
    Is this right?
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