In regards to your question, if the fee for enrolment is being used to pay for the prize, then this will be considered as gambling, hence, deemed not permissible.
The definition of gambling as mentioned in Raddul-Muhtar is: “Gambling is a dealing in which the chance of profit and loss is ambiguous.” (Raddul- Muhtar p.577 v.9)
In gambling the gain of one person is dependant upon the loss of the other. One is sucked dry of his wealth which then reaches the other. The other harms are that one becomes deprived of the habit of livelihood and dreams that he will sit and take what belongs to others. Also gambling, like wine becomes the course of mutual dispute and prevents one from remembering Allah (SWA).
(Maariful-Quran P.548-552 v.2)
The conclusion is that the fee for Enrolment, which is being used to pay for the prize, will not be permissible, because there is a chance of gaining profit (i.e. by winning) and the chance of losing it.
However, if the enrolment fee is being paid to organise the event or pay for the equipments etc and from it a small amount of money is given as a prize, then this will be permissible.
Mohammed Tosir Miah
Darul Ifta Birmingham