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mathmath333

  • one year ago

counting question

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  1. mathmath333
    • one year ago
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    In how man ways can 8 cars be arranged such that there are exactly 4 cars between 2 specified cars.

  2. mathmath333
    • one year ago
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    |dw:1440017302219:dw|

  3. phi
    • one year ago
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    are the "2 specified cars" fixed in those "parking spots"? are we parking 8 cars or 6 cars?

  4. mathmath333
    • one year ago
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    they are just fixed such that 4 cars are between them

  5. mathmath333
    • one year ago
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    |dw:1440017527636:dw| this diadram can also be possible

  6. phi
    • one year ago
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    for each "2 car" situation, there are 6! ways to park the other cars. if we call the 2 cars A and B, there are 3 ways to park A and B with 4 spaces between them and if we swap them, another 3 so 6*6! ways

  7. mathmath333
    • one year ago
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    how did u get red six ->\(\color{red}{6}*6!\)

  8. phi
    • one year ago
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    A _ _ _ _B_ _ _A_ _ _ _ B _ _ _ A _ _ _ _ B and then switch A and B for the other 3

  9. mathmath333
    • one year ago
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    oh i see thanks ,

  10. mathmath333
    • one year ago
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    can i count this one too B _ _A_ _ _ _ from right it has 4 distance

  11. phi
    • one year ago
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    you want exactly 4 cars between 2 specified cars.

  12. mathmath333
    • one year ago
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    oh so i cant count that

  13. phi
    • one year ago
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    no , that is exactly 2 cars between them, so it does not count

  14. anonymous
    • one year ago
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    |dw:1440018099258:dw|

  15. mathmath333
    • one year ago
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    i got confused with that , earlier where number where used instead of cars in some previuos question

  16. phi
    • one year ago
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    it can get confusing. people hate this stuff... it makes their heads hurt.

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