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sh3lsh
 one year ago
How many ways are there to distribute 12 distinguishable objects into six distinguishable boxes so that two objects are placed in each box?
sh3lsh
 one year ago
How many ways are there to distribute 12 distinguishable objects into six distinguishable boxes so that two objects are placed in each box?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0here we must use the fundamental principle of counting...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the first box can actually fill in 12 possible ways...and then the second box can be filled in 11 ways only...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0totally there arre 12*11 ways to fill these boxes... therefore answer=132

kropot72
 one year ago
Best ResponseYou've already chosen the best response.0The number of combinations of the 12 objects taken 2 at a time is found as follows: There are 12 choices for the first object and 11 choices for the second object. Therefore the number of possible pairs is (12 * 11)/2 = 66. Note that we divide by 2, the reason being that the order of choice does not matter. The number of combinations of the 66 pairs taken 6 at a time is given by: \[\large 66C6=\frac{66\times65\times64\times63\times62\times61}{6\times5\times4\times3\times2\times1}=you\ can\ calculate\]

sh3lsh
 one year ago
Best ResponseYou've already chosen the best response.0Unfortunately, the answer is 7,484,400

sh3lsh
 one year ago
Best ResponseYou've already chosen the best response.0This is how to do it if you wanted to know! http://math.stackexchange.com/questions/468824/distinguishableobjectsintodistinguishableboxes In this case, \[\left(\begin{matrix}12 \\ 2\end{matrix}\right) \left(\begin{matrix}10 \\2\end{matrix}\right)\left(\begin{matrix}8 \\ 2\end{matrix}\right)\left(\begin{matrix}6 \\ 2\end{matrix}\right)\left(\begin{matrix}4 \\ 2\end{matrix}\right)\left(\begin{matrix}2 \\ 2\end{matrix}\right)\]
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