# Thread: Number of ways of dividing things into groups...

1. ## 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
$\displaystyle ^n^+^k^-^1C_n$ 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?

2. There is a mistake in the first part. It should be $\displaystyle ^{n+k-1}\mathcal{C}_{k-1}$.

For the second part it is just $\displaystyle k^n$.

3. ## Re: Number of ways of dividing things into groups...

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

4. ## Re: Number of ways of dividing things into groups...

Originally Posted by rickrishav
And what are the number of ways of putting n objects of which $\displaystyle r_1$ are of one type, $\displaystyle r_2$ are of second type and so on, into k number of boxes.
The question implies $\displaystyle r_1+r_2=n~.$
$\displaystyle \binom{r_1+k-1}{r_1}\binom{r_2+k-1}{r_2}$