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?

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.

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 $\displaystyle r_1$ are of one type, $\displaystyle r_2$ are of second type and so on, into k number of boxes.

The question implies $\displaystyle r_1+r_2=n~.$

$\displaystyle \binom{r_1+k-1}{r_1}\binom{r_2+k-1}{r_2}$