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mathmath333

  • one year ago

Counting Problem

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  1. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & \normalsize \text{In how many ways can 4 boys & 4 girls be arranged}\hspace{.33em}\\~\\ & \normalsize \text{such that no 2 girls are together.}\hspace{.33em}\\~\\ \end{align}}\)

  2. anonymous
    • one year ago
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    You can probably make an organized list, or sample space

  3. mathmath333
    • one year ago
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    ok

  4. mathmath333
    • one year ago
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    3 girls together also includes 2 girls together

  5. mathmath333
    • one year ago
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    u mean answer is 2

  6. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & \normalsize \text{In how many ways can 4 boys & 4 girls be arranged in a row}\hspace{.33em}\\~\\ & \normalsize \text{such that no 2 girls are together.}\hspace{.33em}\\~\\ \end{align}}\)

  7. ganeshie8
    • one year ago
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    forget about girls, first you arrange the \(4\) boys

  8. ganeshie8
    • one year ago
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    how many ways can you arrange \(4\) boys ?

  9. mathmath333
    • one year ago
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    4!=24

  10. ganeshie8
    • one year ago
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    Yes |dw:1440079075919:dw|

  11. anonymous
    • one year ago
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    don't mind me - I am not good with this stuff - just read/listen to what @ganeshie8 wrote

  12. mathmath333
    • one year ago
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    5*4=20

  13. IrishBoy123
    • one year ago
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    .

  14. ganeshie8
    • one year ago
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    scratch that

  15. mathmath333
    • one year ago
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    have u also counted this situation gbbgbgbg

  16. ganeshie8
    • one year ago
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    next, for each of that arrangement, the girls can only go between the boys. so there are exactly \(5\) for the \(4\) girls to go : |dw:1440079754229:dw|

  17. ganeshie8
    • one year ago
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    how many ways can you arrange 4 girls in 5 chairs ?

  18. IrishBoy123
    • one year ago
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    .

  19. ganeshie8
    • one year ago
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    In other words, how many 4 letter words can you make using 5 different letters ?

  20. mathmath333
    • one year ago
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    4!

  21. ganeshie8
    • one year ago
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    no, try again

  22. mathmath333
    • one year ago
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    5!

  23. ganeshie8
    • one year ago
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    yes so the final answer is \(4!*5!\)

  24. mathmath333
    • one year ago
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    is their any alternate way for this

  25. ganeshie8
    • one year ago
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    there are many ways to work it the one i showed you is the most simplest one

  26. mathmath333
    • one year ago
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    example using negation of sentense "no 2 girls are together"

  27. ganeshie8
    • one year ago
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    that would only complicate things because you need to consider different cases : 2 girls together, 3 girls together, 4 girls together

  28. ganeshie8
    • one year ago
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    the method i showed you is simple : 1) first place boys 2) next work out where girls can go

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