In how many ways can 5 prizes be distributed among four students when every student can take one or more prizes?
“can” is used to express here possibility. here every student is able to take one or more prizes, can not rule out the possibility of zero prizes.
So they can even take zero prizes. that’s why it is 45 ways. but any way, they could have asked like this. “…………..every student can take any number of prizes” .