Question 120
10 language interpreters are invited to participate in an international mathematical contest. Each of the 10 interpreters is proficient in exactly 2 among the 5 following languages: Greek, Slovenian, Vietnamese, Spanish and German. Furthermore, the combinations of the 2 proficient languages among the 5 are all different for the interpreters. It is decided that the interpreters are distributed into 5 rooms, 2 people per room, in such a way that each pair of the interpreters assigned to the same room shares a common language of proficiency. How many different ways of distributing interpreters satisfy this requirement? Do not distinguish the two arrangements of room assignments in which all the five pairs occupying the same room are identical.