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mathmath333

  • one year ago

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  1. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & \normalsize \text{There are 7 people and 4 chairs. }\hspace{.33em}\\~\\ & \normalsize \text{In how many ways can the chairs be occupied.}\hspace{.33em}\\~\\ \end{align}}\)

  2. amilapsn
    • one year ago
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    We can do that in two steps. 1st step: Choosing 4 people out of 7(Combination ) 2nd step: Seating them.(Permutation)

  3. mathmath333
    • one year ago
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    is it 4!

  4. amilapsn
    • one year ago
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    In my method the answer will be this.(Giving the same as nnesha's result): \(\huge ^7C_4\times 4!\)

  5. mathmath333
    • one year ago
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    1st step: Choosing 4 people out of 7(Combination ) 2nd step: Seating them.(Permutation) How to implement this

  6. amilapsn
    • one year ago
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    \[\huge \ldots=P_{(7,4)} \]

  7. ganeshie8
    • one year ago
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    i like amilapsn's method, but here is an alternative that Nnesha is talking about : you look at 4 chairs, the first chair can have any one of the 7 persons : 7 ways after that, the second chair can have any one of the remaining 6 persons : 6 ways after that, the third chair can have any one of the remaining 5 persons : 5 ways after that, the fourth chair can have any one of the remaining 4 persons : 4 ways so total seating arrangements = 7*6*5*4

  8. ganeshie8
    • one year ago
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    the problem is equivalent to that of finding number of 4 letters words using 7 different letters

  9. mathmath333
    • one year ago
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    i think it as only 4 persons can be seated and the 4 persons can be arranged in 4! ways

  10. amilapsn
    • one year ago
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    Simplicity @ganeshie8 :D lol

  11. ganeshie8
    • one year ago
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    4! is true if you just have 4 chairs

  12. amilapsn
    • one year ago
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    ....and only 4 people..

  13. mathmath333
    • one year ago
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    yes i just have 4 chairs

  14. ganeshie8
    • one year ago
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    ** 4! is true if you just have 4 chairs and 4 people

  15. amilapsn
    • one year ago
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    You can take a simple example like 4 people and 3chairs and get the feeling @mathmath333

  16. amilapsn
    • one year ago
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    people ABCD ok? All possible ways: ABC ACB ABD ADB ACD ADC .... ... Fill in the blanks and you've get the feeling....

  17. mathmath333
    • one year ago
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    is there any website that shows permutations and combinations list

  18. amilapsn
    • one year ago
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    python has got the function permutations in itertools module.

  19. mathmath333
    • one year ago
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    ABC ACB ABD ADB ACD ADC BCD BDC

  20. ganeshie8
    • one year ago
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    you may use this for combinations https://jsfiddle.net/ganeshie8/r2hjr3js/4/

  21. mathmath333
    • one year ago
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    nice

  22. mathmath333
    • one year ago
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    it gave this for abcdefg and 4 comb {a,b,c,d} {a,b,c,e} {a,b,d,e} {a,c,d,e} {b,c,d,e} {a,b,c,f} {a,b,d,f} {a,c,d,f} {b,c,d,f} {a,b,e,f} {a,c,e,f} {b,c,e,f} {a,d,e,f} {b,d,e,f} {c,d,e,f} {a,b,c,g} {a,b,d,g} {a,c,d,g} {b,c,d,g} {a,b,e,g} {a,c,e,g} {b,c,e,g} {a,d,e,g} {b,d,e,g} {c,d,e,g} {a,b,f,g} {a,c,f,g} {b,c,f,g} {a,d,f,g} {b,d,f,g} {c,d,f,g} {a,e,f,g} {b,e,f,g} {c,e,f,g} {d,e,f,g}

  23. ganeshie8
    • one year ago
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    right you should get 7C4 = 35 combinations

  24. ganeshie8
    • one year ago
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    for permutations, notice that each of that combination above can be permuted in 4! ways so number of permutations = 35*4!

  25. mathmath333
    • one year ago
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    is this question same as "In how many ways can a 4 digit number be formed using digits "1,2,3,4,5,6,7"

  26. amilapsn
    • one year ago
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    yep... If you aren't allowed to use the same number twice.

  27. mathmath333
    • one year ago
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    ok thnx

  28. mathmath333
    • one year ago
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    from the past 2 weeks i m getting this very annoying bug I have to reload the page every time to type and my question gets changed to this page

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  29. ganeshie8
    • one year ago
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    you're not alone, everybody is facing that issue @Astrophysics is there any fix yet ?

  30. amilapsn
    • one year ago
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    me too...

  31. mathmath333
    • one year ago
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    lol how can so many people tolerate this

  32. mathmath333
    • one year ago
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    previuosly it happened only once in an hour but recently it get to on every long text i type

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