The tragedy happened at the El Alto University near the Bolivian capital of La Paz, Reuters reported.
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A horrifying video of the incident shows a crowd of students pushing and shoving each other. A metal railing gives way, causing multiple students to plummet four stories below.
A few students could be seen dangling off the side before being pulled to safety as the crowd disperses.
Health Minister Jayson Auza told reporters that "seven have died and five are in a critical state, some of them stabilized."
Bolivia’s Special Force to Fight Crime has opened an investigation. The crime unit says the victims' ages ranged from 19 to 27.
Local media reported that the students were in the middle of a tense meeting – which had prompted some physical altercations – at the university before the railing broke.