How many ways are there to pack $9$ identical DVDs into $3$ indistinguishable boxes so that each box contains at least two DVDs?
Is this having one to one correspondence with the partitions of a number?
Yes, it's the number of partitions of $3$ with at most $3$ parts, but since $3\leq3$ the extra condition doesn't add anything in this case.
(The first $3$ is the number of DVDs you have left after putting the minimum number into each box, and the second is the number of boxes.)
So there are $3$ ways, which correspond to the partitions $3$, $2+1$, $1+1+1$, and have boxes with $5,2,2$ or $4,3,2$ or $3,3,3$ DVDs respectively.