how many ways are there to put 36 non-distinguishable balls in 15 distinguishable buckets? This is what I thought: suppose the balls are distinguishable. every time you want to put a ball in a bucket, you have 15 possibilities. so if you have to do this 36 times, you have 15^36 ways to do this. Suppose then that the balls are non-distinguishable, then you have 15^36/15!.
Is this the correct way to think about this problem?