Question

5 Five persons wearing badges with numbers 1,2,3,4,5 are seated on 5 chairs around a cir-
cular table. In how many ways can they be seated so that no two persons whose badges have
consecutive numbers are seated next to each other? (Two arrangements obtained by rotation
around the table are considered different.)
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Answer 1

There are two for that by which no two consecutive no. bandage people can sit together are :

(1) 13524

(2) 15324