Packing $8$ identical DVDs into $5$ indistinguishable boxes I am trying to solve this question:

How many ways are there to pack eight identical DVDs into five indistinguishable boxes so that each box contains at least one DVD?

I am very lost at trying to solve this one. My attempt to start this problem involved drawing 5 boxes, and placing one DVD each, meaning 3 DVDs were left to be dropped, but I am quite stuck at this point.
Any help you can provide would be great. Thank you.
 A: You are nearly finished. We have three DVD to dump into boxes. Maybe we put all $3$ in the same box. Maybe we use a $2$-$1$ split. Or maybe we use a $1$-$1$-$1$ split.  Since the boxes are indistinguishable, we have a total of three possibilities.
A: This is same as number of ways of writing as a sum of 5 positive integers (order does not matter since the boxes are indistinguishable). In short we want the 5 partitions of 8, $P(8,5)$. Using the recurrence relation $$P(n,k) = P(n-k,k)+P(n-1,k-1)$$ we get $P(8,5) = P(3,5)+P(7,4)$. Clearly, $P(3,5) = 0$. Using the recurrence we compute $P(7,4) = 3$. The three possible ways are $(1,1,1,1,4), (1,1,1,2,3), (1,1,2,2,2)$.
A: Identical objects in indistinguishable(identical) boxes. 
Use partition of numbers but $x_1 \geq x_2 \geq x_3 \geq x_4 \geq x_5 \geq 1$ since $(3,0,0,0,0)$ is the same as $(0,3,0,0,0)$ //identical offices.
Now $$x_1+x_2+x_3+x_4+x_5=8$$ but $x_i' = x_i-1$  so all $x_i'\geq 0$.
Hence, $$x_1'+x_2'+x_3'+x_4'+x_5'=3 =8-(5 \cdot 1)$$
So, $$(x_1',x_2',x_3',x_4',x_5') \in \{(3,0,0,0,0),(2,1,0,0,0),(1,1,1,0,0,0)\}$$
Ans) 3 ways.
NOTE: Stirling's Number(first or second kind depends on the problem) is for distinct objects in identical boxes. 
A: 5 boxes 8 dvds ... 
firstly you put one dvd in each box .
and now you solve no. of ways of placing 3 dvds in 5 boxes.
which is same as no of solution to the equation 
    b1 + b2 + b3 + b4 + b5 = 3  i.e., 
$ (5+3-1)\choose (3)$ = 35 .  .... [solution to the equation a1+a2+a3+...an = r is $ (n+r-1) \choose n $ which can easily be proved]
 so 35 ways
A: It is called stirling numbers.
 S(8,5)=1050 ways
