nafil qurbaani

Few people slaughtering one sheep for Rasululullah (Sallallahu Alayhi Wasallam)

Q: A group of students get together to get a sheep slaughtered for Qurbaani for the Prophet (Sallallahu Alayhi Wasallam). Will the Qurbaani be invalid since a group of people cannot slaughter a single sheep, or will it be valid since if they intended the slaughter to be on behalf of a single person (i.e. the Prophet (Sallallahu Alayhi Wasallam)?