At the pizza restaurant... The five friends Abe, Bob, Carl, Dwayne, and Eddy fin

Question

At the pizza restaurant... The five friends Abe, Bob, Carl, Dwayne, and Eddy finally make it to the restaurant to get their pizza. Interestingly, the restaurant has only circular tables and-bonus! -each table has only 5 chairs. Once the friends got themselves seated, Abe asked "l wonder how may ways there are for us to sit around the table if we don't count arrangements where everyone has the same left neighbor and the same right neighbor as different?" Realizing there was no way around it, the friends started to dutifully shuffle around the table, changing seats and counting the whole time. How many different arrangements did they come up with?

Explanation / Answer

Fix a person then we are left with 4 persons. Hence there will be 4! ways of arrangements they can sit with and which is 24

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