In our math class today, we had a disagreement regarding factorials in this question:
Six students in a speech class will have to give their speech on the same day. One of the students insists on being first. If this student's request is granted, how many different ways are there to schedule the speeches?
Some students stated that the answer should be $5!$ while the provided answer key says it should be $6!$
$5!$, we no longer have any more decision to make for the first student anymore.
To make it even clearer, suppose there are only $2$ students and one student insists to be the first. If the wish is granted, then there is only $1!$ possibility.