Question

If 8 identical blackboards are to be divided among 4 schools, how many divisions are possible? how many if each school must receive at least 1 blackboard?

Answer 1

Alright, so we'd use the combinations with repetition formula, so we choose from 4 schools to distribute to and distribute 8 blackboards. It's then 

( 8+4-1)!/8!(4-1)!=11!/(3!*8!)=165

For at least one blackboard, we first distribute 1 to each school and then have 4 blackboards left, getting (4+4-1)!/4!(4-1)!=7!/(4!*3!)=35