PROBLEM: How many ways can 10 identical DVDs be put in 3 identical boxes so that each box contains at least 2 DVD's.
My reasoning is this ..
Since each box must contain at least 2 DVDs, I take 3 out of the 10 DVDs out and automatically assign each of them to a box. So now all the boxes have 1 DVD, and now 7 are left.
The problem has now been reduced to how many ways can you assign 7 DVDs into 3 boxes so that each box gets at least 1 DVD. So here using stars and bars, you can use 2 bars to create 3 partitions of the 7 DVDs. Between the 7 DVDs there are 6 spots to put the 2 bars in. This yields 6 choose 2 combinations which is 15.
The correct answer is 4, Im lost, could someone please explain.