There are four balls of different colours and four boxes of colours, same as those of the balls. The

Question

There are four balls of different colours and four boxes of colours, same as those of the balls. The number of ways in which the balls, one each in a box, could be placed such that a ball does not go to a box of its own colour is

Professor PC Thomas Classes · Answer

Required number of ways\ $=P(4,3)+P(3,2)+P(2,1)$\ $=\frac{4!}{3!1!}+\frac{3!}{2!1!}+\frac{2!}{1!1!}=4+3+2=9$\