In how many ways can 5 prizes be distributed among 4 boys when every boy can take one or more prizes?

Step-by-step solution

First prize may be given to any one of the 4 boys, hence first prize can be distributed in 4 ways. similarly every one of second, third, fourth and fifth prizes can also be given in 4 ways. the number of ways of their distribution =4 4 4 4 4=4⁵=1024