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 gbc-mfti-uck​

Answer 1

Answer:

Step-by-step explanation:

maximum number of hats used of same are 2.They can not be 3 otherwise atleast 2 hats of same colour are consecutive  

Now,Let hats used are R,R,G,G,B

(which can be selected in 3 ways .it can be RGGBB or RRGBB also )

Now numbers of ways of distributing blue hat (single one ) in 5 Person equal to 5 let blue hast goes to person A.

Now either position B and D are filled by green hats and C and E are filled by reds hats or B and D are filled by Red hats and C and E are filled by green hats  

⇒2 ways are possible  

Hence total number of ways =3×5×2=30 ways