What is the ruling of Islamic law regarding female students going on mixed trips with their female friends, under the pretext that it is their last year and for recreation?

A woman is not permitted to travel without a mahram, and this includes any travel, regardless of its duration. Similarly, mixed travel between young men and women is forbidden by Islamic law due to the fitnah (temptation/strife) that results from it. Islam does not prohibit recreation but restricts it to what is permissible by the Sharia.