There are 4 routes between Delhi and Patna. In how many different ways can a man go from Delhi to Patna and return, if for returning
(i) any of the routes is taken;
(ii) the same route is taken ;
(iii) the same route is not taken ?
Sham can take any one of three routes from school (S) to the town center (T), and can then take four possible routes from the town center to his home (H). He doesn't retrace his steps. How many different possible ways can Sham walk home from school?