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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?

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  1. anonymous
    • one year ago
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    hello friend

  2. anonymous
    • one year ago
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    here we must use the fundamental principle of counting...

  3. anonymous
    • one year ago
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    the first box can actually fill in 12 possible ways...and then the second box can be filled in 11 ways only...

  4. anonymous
    • one year ago
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    totally there arre 12*11 ways to fill these boxes... therefore answer=132

  5. kropot72
    • one year ago
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    The 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: \[\large 66C6=\frac{66\times65\times64\times63\times62\times61}{6\times5\times4\times3\times2\times1}=you\ can\ calculate\]

  6. sh3lsh
    • one year ago
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    Unfortunately, the answer is 7,484,400

  7. sh3lsh
    • one year ago
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    This is how to do it if you wanted to know! http://math.stackexchange.com/questions/468824/distinguishable-objects-into-distinguishable-boxes 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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