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mathmath333

  • one year ago

The number of ways in which four particular persons A,B,C,D and six more persons can stand in a queue so that A always stands before B, B before C, and C before D, is ?

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  1. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & \normalsize \text{ The number of ways in which four particular persons A,B,C,D }\hspace{.33em}\\~\\ & \normalsize \text{ and six more persons can stand in a queue so that A always }\hspace{.33em}\\~\\ & \normalsize \text{ stands before B, B before C, and C before D, is ? }\hspace{.33em}\\~\\ \end{align}}\)

  2. dan815
    • one year ago
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    |dw:1442643874411:dw|

  3. mathmath333
    • one year ago
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    this is one of the case

  4. mathmath333
    • one year ago
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    |dw:1442644105548:dw|

  5. dan815
    • one year ago
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    10!/4!

  6. dan815
    • one year ago
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    there are 10! ways to arrange these 10 persons now for each of those arrangements there is some arrangement of ABCD 4! ways of them, we only want the arrangement A B C D so 1 for every one of thsoe 4! ways thus 10!/4!

  7. mathmath333
    • one year ago
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    but the ABCD can be in many ways like this |dw:1442644275123:dw|

  8. dan815
    • one year ago
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    do you want clearer explaination

  9. dan815
    • one year ago
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    for example lets take some random arrangement in 10! 1 2 3 4 A 5 B 6 C D okay for this arrangement there are 4! other ways we count when A B C D can be placed in way , and the numbers 1 to 6 are left in same spot

  10. mathmath333
    • one year ago
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    is this (below) a valid set up|dw:1442644423498:dw|

  11. dan815
    • one year ago
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    we count that in the 10!

  12. dan815
    • one year ago
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    so taking 1 for every 4! we will take only the A B C D case for each of those arrangements in 10!

  13. mathmath333
    • one year ago
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    ok

  14. dan815
    • one year ago
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    you have any questions about this?

  15. mathmath333
    • one year ago
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    let me read and think

  16. dan815
    • one year ago
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    ill make it clearer okay

  17. dan815
    • one year ago
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    for 10! ways we will have the arrangement of every single possible way of placing these 10 people

  18. dan815
    • one year ago
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    let us look at some of these arragenment sequences

  19. dan815
    • one year ago
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    |dw:1442644766778:dw|

  20. dan815
    • one year ago
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    there are 4! ways for this one arrangement of how you play these 6 people in the 10 spots

  21. dan815
    • one year ago
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    out of these 4! ways , we only want one of them where its A B C D

  22. dan815
    • one year ago
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    so another way less intuitive would now be this means all we care about is how we place the 6 people in the 10 spots

  23. mathmath333
    • one year ago
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    ok i got it

  24. dan815
    • one year ago
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    ok

  25. mathmath333
    • one year ago
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    |dw:1442645081498:dw|

  26. dan815
    • one year ago
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    welcome!

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