When three people sit and eat a meal together, they make a Zimun before Birkat Ha’mazon. When ten people eat a meal together, they recite a Zimun as a Minyan, with the word "Elokenu." The question arises as to whether Yeshiva students sitting at different tables in the cafeteria combine to make a Minyan for a Zimun. Do we view the students at different tables as separate groups, such that they do not combine to form a Minyan, or are they viewed as sitting all together in one group?
Rav Yishak Yaakov Weiss (1901-1989), in his Minhat Yishak (8:8), ruled that the students are all considered part of the same group, despite sitting at separate tables, and thus may recite the Zimun as a Minyan, with "Elokenu." Others, however, disagree. Hacham Bension Abba Shaul (Israel, 1923-1998), in his work Or Le’sion (vol. 2, p. 114), claimed that yeshivah students eating in a cafeteria do not combine to form a Minyan even if they sit at the same table, because they all follow different schedules. Students come, eat and leave at their convenience, without necessarily intending to sit together, and thus unless they clearly express their intent to sit together as a group, students eating in a cafeteria do not form a Minyan.
In light of these different opinions, the Yalkut Yosef (vol. 3, p. 377; listen to audio recording for precise citation) rules that Yeshivah students should make a point of expressing their intent to eat together when they sit down in the cafeteria. This way, they avoid this Halachic question and can recite the Zimun as a Minyan according to all opinions.
This applies only when the students eat in a cafeteria. When students eat together in a classroom, however, they can recite a Zimun as a Minyan even if they do not explicitly state their intent to eat together. This is the ruling of Rav Shlomo Zalman Auerbach (Jerusalem, 1910-1995), in his Minhat Shelomo (60:5). Rav Shlomo Zalman followed the view that Yeshiva students in a cafeteria do not combine to form a Minyan, but he writes that when students eat together in a classroom, they are considered a group and thus form a Minyan.
Summary: When Yeshivah students sit down together in a cafeteria for a meal, they should express their intent to eat together, so that they can recite Zimun as a Minyan according to all opinions. Without this explicitly stated intent, they are not considered a group and thus cannot recite the Zimun as a Minyan according to some Halachic authorities.
