8 identical blackboards are divided among 4 schools:

1) what are the # of divisions possible?

using combination with repetition formula $\displaystyle \binom{n+k-1}{n-1}$

I get $\displaystyle \binom{8+4-1}{4-1} = \binom{11}{3}$

2) how many divisions are possible if each school receives at least 1 blackboard?

$\displaystyle \binom{8-1}{4-1} = \binom{7}{3}$

NOW FOR MY QUESTION:

I was curious to what would happen if it was asked: how many divisions are possible if each school receives at least 2 blackboards?

would it just be:

$\displaystyle \binom{8-2}{4-1} = \binom{6}{3}$

Thanks for any input