Try this beautiful problem from the PRMO, 2019 based on Two arrangements.
Five persons wearing badges with numbers 1,2,3,4,5 are seated on 5 chairs around a circular table. Find the number of ways they be seated that no two persons whose badges have consecutive numbers are seated next to each other.
Arrangement
Algebra
Number Theory
Answer: is 10.
PRMO, 2019, Question 5
Combinatorics by Brualdi
Here they may seat in circular way such that 1,3,5,2,4 and again 1
then they may seat in another circular way 1,4,2,5,3 and again 1
Then number of ways = (2)(5) =10.
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