I had this task a while ago; let's say I have 15 balls (5 in three different colors) and 3 identical boxes, in how many different ways can I place the balls in the boxes?
What I thought of was just following the formula for combinations with repetition like:
(n+k-1) choose k
but I got the wrong answer. Instead I was supposed to use something like:
(n+k-1) choose (k-1)
to calculate x1+x2+x3=15 but I don't understand the difference in these approches.
Sorry if I sound unclear somehow but I find it really hard to explain since I'm so confused as well.
Thanks in advance!