I'm a circus performer, currently working in a show which has 5 roles in it. In the cast we have 7 performers who change roles daily so that two people get a day off every day. We have been trying to work out how many combinations are possible with factorials, but we don't know how to constrain the 7 performers to the 5 roles. Let me know if that doesn't make sense, but if you know the answer, please show your working too! Thanks in advance!
2026-04-08 00:46:24.1775609184
Amount of combinations out of seven when only five can be in at one time
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Assuming order doesn't matter, the answer is $7\choose5$ = $\frac{7!}{2!5!}$