mathmath333
  • mathmath333
Counting problem
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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mathmath333
  • mathmath333
\(\large \color{black}{\begin{align}& \normalsize \text{The number of ways in which a Chairman and a Vice-Chairman can be chosen}\hspace{.33em}\\~\\ & \normalsize \text{from amongst a group of 12 persons assuming}\hspace{.33em}\\~\\ & \normalsize \text{that one person can not hold more than}\hspace{.33em}\\~\\ & \normalsize \text{one position.}\hspace{.33em}\\~\\ \end{align}}\)
ali2x2
  • ali2x2
this is off a google book xD
anonymous
  • anonymous
do you know C notation?

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ganeshie8
  • ganeshie8
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
anonymous
  • anonymous
Using C notation:\(^{12}C_2\times2\)
mathmath333
  • mathmath333
what does it mean by \(\large \color{black}{\begin{align} & \normalsize \text{assuming that one person can not hold more}\hspace{.33em}\\~\\ & \normalsize \text{ than one position is ?}\hspace{.33em}\\~\\ \end{align}}\)
ganeshie8
  • ganeshie8
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
anonymous
  • anonymous
It says one person can't be president and vice at the same time!
anonymous
  • anonymous
Thank you @ganeshie8 and @mathmath333 for meddling me!!
ganeshie8
  • ganeshie8
:) 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
mathmath333
  • mathmath333
also notice that \(\large ^{12}P_{2}=132\)
ganeshie8
  • ganeshie8
Yep, all those interpretations are equivalent
ganeshie8
  • ganeshie8
we have \[\large ^nP_r~ ~=~~ ^nC_r * r!\]

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