Number of ways of dividing things into groups...

• November 3rd 2010, 11:21 PM
rickrishav
Number of ways of dividing things into groups...
Suppose I have n number of identical objects and I want to distribute them into k number of boxes there are
$^n^+^k^-^1C_n$ ways to do so, with no constrains upon the number of balls in the boxes.

Now if I have n non identical objects and k boxes what should be the number of ways to distribute the objects?
• November 4th 2010, 05:09 AM
Plato
There is a mistake in the first part. It should be $^{n+k-1}\mathcal{C}_{k-1}$.

For the second part it is just $k^n$.
• October 3rd 2011, 11:37 PM
rickrishav
Re: Number of ways of dividing things into groups...
And what are the number of ways of putting n objects of which $r_1$ are of one type, $r_2$ are of second type and so on, into k number of boxes.
• October 4th 2011, 04:49 AM
Plato
Re: Number of ways of dividing things into groups...
Quote:

Originally Posted by rickrishav
And what are the number of ways of putting n objects of which $r_1$ are of one type, $r_2$ are of second type and so on, into k number of boxes.

The question implies $r_1+r_2=n~.$
$\binom{r_1+k-1}{r_1}\binom{r_2+k-1}{r_2}$