If I were to do it, I would do it like this.

#1: I'd create a list of the students participating, and give them each a number. For this example, I'll just have a bunch of students that are numbered.

Student 1
Student 2
Student 3
Student 4
Student 5
Student 6

#2: I have six students, So I will roll a 1d5 to see which of the students will be paired with student 6.

#3: I look at my roll and save the link to show that I'm not a cheater acting out of bias. [url=https://www.roleplayerguild.com/rolls/23520]But it's a 4[/url], so student 6 is going to get paired with student 4

#4: I move all of the students into their new positions. Because student 4 got paired up with 6, 5 moves into student 4's old position. Not that it matters in this example, as we will be rolling for their partner, so their position is irrelevant. And since we only have 3 students left, we can roll a d3 to see who it will be.

Student 1
Student 2
Student 3
Student 5 (4)

#5: Continue rolling as necessary. Though for this example, there would only be two students left after this selection, so there would be no reason to do more rolls. 

#6: Publicly announce the results, watch people ICly and OOCly scream.