Is it obligatory to fulfill a vow to slaughter a sheep for the female students if the Radiology course is offered, knowing that the vow was agreed upon during a break?

Your statement to the female students: "If the subject is opened, I will slaughter a sheep for you" is not considered a vow unless you intended it as an act of drawing closer to Allah Almighty by feeding people and uttered words that convey this meaning. However, if you merely intended to slaughter for them, it is not considered a vow, but rather a promise that is commendable to fulfill.