## 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?

1. anonymous

hello friend

2. anonymous

here we must use the fundamental principle of counting...

3. anonymous

the first box can actually fill in 12 possible ways...and then the second box can be filled in 11 ways only...

4. anonymous

totally there arre 12*11 ways to fill these boxes... therefore answer=132

5. kropot72

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

Unfortunately, the answer is 7,484,400

7. sh3lsh

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, $\left(\begin{matrix}12 \\ 2\end{matrix}\right) \left(\begin{matrix}10 \\2\end{matrix}\right)\left(\begin{matrix}8 \\ 2\end{matrix}\right)\left(\begin{matrix}6 \\ 2\end{matrix}\right)\left(\begin{matrix}4 \\ 2\end{matrix}\right)\left(\begin{matrix}2 \\ 2\end{matrix}\right)$