Entrance is free ... members.

[Nonverbis]

Upstream Proficiency by Virginia Evans and Janny Dooley.

Task: Fill the gapswith suitable prepositions.

Entrance is free ... members.

The answer key gives "to".

I inserted "for".

But the dictionary gives two variants: https://www.oxfordlearnersdictionaries.com/definition/english/free_1?q=free

free to somebody Use of the pool is free to members.
free for somebody Updates are free for registered users.

Could you tell me whether two variants are possible here or not?

 

[5jj]

Yes.

 

[GoodTaste]

Are there any difference between the two?

 

[Rover_KE]

No.

 

[emsr2d2]

Are Is there any difference between the two?

See above. If you want to use "Are" at the start, you need to use "differences".

 

[Tdol]

Both would be allowed in the exam- sometimes, books don't consider every possibility.