Charging a fee, or even making a "profit" for the trip does not disqualify you from becoming tax exempt. It's what you do with the funds that are the "profit".
You can even have paid employees. But the profit should be going to the benefit of a charitable reason, e.g. scholarships, school supplies, and other recognizable charitable reasons, which can include things like school spirit (social parties), if careful how you do it.
A parent group in our school sponsors a safe, alcohol-free graduation trip. The group originally incorporated, but did not get their 501(c)3. No tax returns of any kind have been filed. In the past, the group raised funds so that the students paid only a token amount to go on the trip. This year the parents decided to eliminate the fund raising. Instead, they calcuated the cost per student and are selling tickets. Can a group like this get recognized as a tax exempt organization? The group has a charitable purpose, but can an organization qualify if its income comes from charging a fee?