self Maths Puzzle

18 chairs are arranged around a hexagon such that there are 3 chairs per side. If 18 men are to be seated on these chairs, then how many different arrangements are possible?

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self Other Question

Six people A, B, C, D, E and F are to be seated at a circular table. In how many ways can this be done if A must always have either B or C on his immediate left and B must always have either C or D on his immediate left? Using the digits of the decimal system, how many numbers lying between 5000 and 6000 (both inclusive), can be forme if,
(i) Repetition of digits is not allowed.
(ii) Repetition of digits is allowed.