I shall provide you with full information on the usage of the verbs ''allow'', ''permit'' and ''let'', as follows:
--> ''Allow'', ''permit'', and ''let'' are all used to say that someone is given permission to do something, or is not prevented from doing something. ''Permit'' is a formal word.
1) ''Allow'' and ''Permit'': both of these verbs are followed by an object and a to-infinitive clause.
E.g.: ''He allowed me to take the course''.
E.g.: ''They do not permit students to use calculators in exams''.
* You can say that people are not allowed to do something or are not permitted to do something.
E.g.: ''Visitors are not allowed to take photographs in the museum''.
E.g.: ''Children are not permitted to use the swimming pool''.
** You can also say that something is not allowed or that it is not permitted.
E.g.: ''Running was not allowed in the school''.
E.g.: ''Picnics are not permitted in the park''.
2) ''Let'': this verb is followed by an object and an infinitive without to.
E.g.: ''Let me go to the party on Saturday. I won't be late''.
E.g.: ''Hey! Let me carry those bags for you!''
*** You don't usually use 'let' in the passive. Do not ever say, for example, 'She was let go to the party'.
--> May I provide you with additional information?
3) ''Enable'': Do not confuse any of the previous words with ''enable''. ''To enable'' someone to do something means to give them the opportunity to do it. It does not mean to give them permission to do it.
E.g.: ''Contraception enables women to plan their families''.
E.g.: ''The new test should enable doctors to detect the disease early''.
Hope that helps! :)
Should you have any further doubts, do not hesitate to contact me. I shall be pleased to help.