In how many ways can 4 prizes be distributed among 5 students, if no student gets all the prizes?

Explanation

The number of ways in which the 4 prizes can be given away to the 5 students, if a student can get any number of prizes `=5^(4)=625`
Again, the number of ways in which a student gets all the 4 prizes=5, since there are 5 students and any one of them may get all the four prizes.
therefore, the required number of ways in which a student does not get all the prizes=625-5=620.