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Five person A,B,C,D and E are selected in a circular arrangement. If each of them is given a hat of one of the three colours red, blue and green, then the number of ways of distributing the hats such that the persons seated in adjacent seatas get different coloured hats is ...................

Answer»


Solution :Given that , no two persons SITTING ADJECENT in circular arrangement ,have hats of same colour, so, only possible combination due to circular arrangement is `2+2+1`.
So, there are following THREE cases of selecting hats are `2R+2B+1Gor 2B+2G+1Ror 2G+2R+1B`.
To distribute these 5 hats first we will select a person which we can done in `3.^C_(1)` ways and distribute that the which is one of it's colour. and now the remaining four hats can be DISTRIBUTED in two ways.
So, total ways will be `3xx.^5C_1xx2 =3xx5xx2=30`


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