Hat Check Problem - IA

Hi, for my IA I was thinking of doing the hat check problem. Essentially it goes like this; group of men walk into a restaurant checking in n number of hats at the door. The restaurant mixes the the hats up and as the evening is over, each man is randomly given a hat from the pile. What is the probability that no person gets their hat back?

Suprisingly, the answer is 1/e.

If anyone is familiar with the problem could you please elaborate on whether this is SL level or above. I have found some explanations rather complicated and wondered whether it was ultimately worth it given the amount of energy it would require with mocks coming up. I know I would be able to get my head around it, but have begun to doubt whether the return (in terms of marks) for this question would be worth it.

I have time to change my topic so I am not particularly worried.

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