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![]()