Five persons $A, B, C, D$ and $E$ are seated in a circular arrangement. If each of them is given a h

Question

Five persons $A, B, C, D$ and $E$ are seated 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 seats get different coloured hats is

Professor PC Thomas Classes · Answer

(30) : We can have 3 possibilities: Red-1, blue-2, green-2; Red-2, blue-1, green-2;\ Red-2, blue-2, green-1\ Now, number of ways for first combination is ${ }^{5} C_{1} 	imes 2=10$\ So, the total number of ways $=10 	imes 3=30$.\