Puzzle #210: Class Groups

There are eight students in a class. There is a project assignment which is to be completed by teams of two students. How many ways can the students be grouped into four pairs?

(Warning: 1&2, 3&4, 5&6, 7&8 and 4&3, 7&8, 2&1, 6&5 are the same grouping.)

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, June 14, 2017 at noon Pacific Time. I will post the answer shortly after.