Correct spelling


Correct spelling, explanation: enrolment is a noun made out of a verb enroll and a noun suffix -ment. As in many similar cases, the process is simple and nothing is changed neither in the base word nor in the suffix. Enrol + -ment = enrolment. Simple as that!

Definition of enrolment:
1. To officially become a member of a school/organization/course etc.
I decided that the enrolment at the nearest university is a good idea because I didn’t want to move out from home yet.
Enrolment had risen sharply during the last three years.

Incorrect spelling


Incorrect spelling, explanation: enrolement is incorrect because it suggests a different base form than it should be. If enrolement was a correct form, there would have to be a verb to enrole, which as of now does not exist.