A new flag is to be designed with six vertical strips using some or all of the colours yellow, green, blue and red. Then, the number of ways this can be done such that no two adjacent strips have the same colour is

A new flag is to be designed with six vertical stripes using some or all of the colour yellow, green, blue and red. Then, the number of ways this can be made such that no two adjacent stripes have the same colour is

Five persons A, B, C, D & E are seated in a circular arrangement. If each of the is given a hat of one of the three colours red, blue & green, then the numbers of ways of distributing the hats such that the person seated in adjacent seat gets different coloured hats is

In how many ways can the following diagram be coloured subject to the following conditions ? No two adjacent regions receive the same colour .

How many minimum number of colours will be required to paint all the sides of a cube without the adjacent sides having the same colours?