We use 'can' or 'may' to give permission. 'May' is formal and used mainly in writing: 'Any person over 18 years may/can apply to join the club.' They can also be used when asking permission: 'Can I take your umbrella? ~ Of course you can.' 'May we come in?~ Of course.' 'May' is used also to express possibility (= perhaps): 'She may be in the cafeteria.' (= Perhaps she is in the cafeteria.) 'Can' is also used to express possibility. However it is quite different from the possibility expressed by 'may': You can ski in on the hills. (There is enough snow.) = It is possible (circumstances permit.) "She may be in the cafeteria." = "She COULD BE be in the cafeteria." Now both sentences express the same meaning (you can use 'could be' instead of 'may/might be' to mean 'perhaps').

She may be in the cafeteria means she is possibly in the cafeteria She can be in the cafeteria means she can be in the cafeteria by permission or she is able to be in the cafeteria where as the others cann't.