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I tried to first finding the probability that only one couple sits together (9x2!8!) then two couples (25x2!2!2!6!) then three (22x3!2!2!2!4!) then four (14x4!2!2!2!2!) then five (5!x2!2!2!2!2!)

I think I would then use the inclusion exclusion principle and divide by 10! to find the probability, but I've never used it with five items. Am I on the right track? How would I finish this?

Thank you so much!

TutorV
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  • The punchline is that, yes inclusion-exclusion is the suggested approach, but your values appeared off, specifically your $9,25,22,14$. It is unclear where you got those values. – JMoravitz Oct 19 '23 at 16:47

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