3) If 3 colours Red, Blue and Green are to be painted on a cube such that all colours are present, Find the number of ways of doing ?
Sol: The process is as follows:
(i) All faces are painted equally - 3 Adjacent faces are painted in 3 different colours
=> Each of the 3 other faces can be painted with any of the 3 colours => 3x3x3 = 27 ways
(ii) All faces are painted unequally
=> 4 Red, 1 Green, 1 Blue (or) 4 Green, 1 Red, 1 Blue (or) 4 Blue, 1 Green, 1 Red