# Thread: questions in combination - help!!!

1. ## questions in combination - help!!!

1. how many posibilities to divide 10 identical white balls and 10 identical black balls to five different boxes

2.how many posibilities to divide 10 identical white balls and 10 identical black balls to five different boxes that every box have at least 1 ball

3.how many posibilities to divide 10 identical white balls and 10 mixed color different balls to five different boxes

2. Originally Posted by tukilala
1. how many posibilities to divide 10 identical white balls and 10 identical black balls to five different boxes

2.how many posibilities to divide 10 identical white balls and 10 identical black balls to five different boxes that every box have at least 1 ball
There $\displaystyle {{N+k-1}\choose N}$ ways to place N identical objects into k different cells.
For your balls, N=10 and k=5.
You need to square the number for one colour. WHY?

There $\displaystyle {{N-1}\choose {N-k}}$ ways to place N identical objects into k different cells with no empty cell.