hello

the problem is that suppose i have n distinct balls(or anything) in a box..i have to take r samples ...i.e i have to pick r balls out of those n one by one ...now there are four cases

1.i take the the mth ball without replacing the previous m-1 balls and the sequence in which i take the balls matters

2.same as one but here the sequence doesnot matter

3. i replace the previously taken balls before picking out the next one and the sequence in which they come out matters

4.same as 3 but the sequence doesnot matter

problem is that in each case in how many possible ways the balls can be organized ...or we can say that in each case how many elements are there in sample space ....

now first three cases i have a general solution for them and i understand them ...but in case of 4th i know the answer but dont know how it came up

..the ans is

$\displaystyle

\binom{n+r-1}{r}

$