In how many ways can 5 different balls be distributed among three boxes?

In how many ways can 4 different balls be distributed among 5 different boxes, when i. no box has more than one ball. ii.a box can have any number of balls. iii. No box contains all the balls

In how many ways can 9different books be distributed among three students if each receives atleast 2 books?

In how many ways can 8 different books be distributed among 3 students if each receives at least 2 books ?

In how many ways can 6 different books be distributed among 3 students such that none get equal number of books

In how many ways can 21 identical blankets be distributed among three beggars so that exactly two of them get equal number of blankets.