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mathmath333

  • one year ago

Counting problem

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  1. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align}& \normalsize \text{The number of ways in which a Chairman and a Vice-Chairman can be chosen}\hspace{.33em}\\~\\ & \normalsize \text{from amongst a group of 12 persons assuming}\hspace{.33em}\\~\\ & \normalsize \text{that one person can not hold more than}\hspace{.33em}\\~\\ & \normalsize \text{one position.}\hspace{.33em}\\~\\ \end{align}}\)

  2. ali2x2
    • one year ago
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    this is off a google book xD

  3. anonymous
    • one year ago
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    do you know C notation?

  4. ganeshie8
    • one year ago
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    First choose chairman, there are \(12\) ways of doing this. After that, choose vice-chairman, there are \(11\) ways of doing this. So both can be done together in \(12\times 11\) ways

  5. anonymous
    • one year ago
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    Using C notation:\(^{12}C_2\times2\)

  6. mathmath333
    • one year ago
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    what does it mean by \(\large \color{black}{\begin{align} & \normalsize \text{assuming that one person can not hold more}\hspace{.33em}\\~\\ & \normalsize \text{ than one position is ?}\hspace{.33em}\\~\\ \end{align}}\)

  7. ganeshie8
    • one year ago
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    Notice that the order in which you chose the ppl didnt matter here, end of the day all you care about is who were picked for chairman and vice-chairman, not the order in which you pick them

  8. anonymous
    • one year ago
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    It says one person can't be president and vice at the same time!

  9. anonymous
    • one year ago
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    Thank you @ganeshie8 and @mathmath333 for meddling me!!

  10. ganeshie8
    • one year ago
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    :) notice that \(^{12}C_2*2 = 12*11\) which is same as the number of different strings of length \(2\) formed by picking letters from a set of \(12\) different letters. @mathmath333

  11. mathmath333
    • one year ago
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    also notice that \(\large ^{12}P_{2}=132\)

  12. ganeshie8
    • one year ago
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    Yep, all those interpretations are equivalent

  13. ganeshie8
    • one year ago
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    we have \[\large ^nP_r~ ~=~~ ^nC_r * r!\]

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