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mathmath333
 one year ago
Counting question
mathmath333
 one year ago
Counting question

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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0\(\large \color{black}{\begin{align} & \normalsize \text{The number of ways of dividing 10 different balloons }\hspace{.33em}\\~\\ & \normalsize \text{in two groups each containing 5 balloons is ? }\hspace{.33em}\\~\\ \end{align}}\)

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1I think that the requested number is: \[\Large 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 = \left( {\begin{array}{*{20}{c}} {10} \\ 5 \end{array}} \right) \cdot 5!\]

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0but answer given is \(\large \dfrac{10!}{5!5!2!}\)

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0sometimes their is typo in book too

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1I don't think that it is a typo, I think that my answer is incorrect!

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1if we have n elements, then for each subset of k elements I have a subset of nk elements, we have: \[\Large \left( {\begin{array}{*{20}{c}} n \\ k \end{array}} \right) = \left( {\begin{array}{*{20}{c}} n \\ {n  k} \end{array}} \right)\]

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0this applies for n different elements right

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1yes! In our case we have n=10 and k=5

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1I think that the requested number of ways is given by the total number of subset divided by 2=2!

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1sinceeach way, gives two subsets of 5 elements
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