Four cities are connected by a road network as shown in the figure. In how many ways can you start from any city and come back to it without travelling on the same road more than once?
Explanation:
It can be seen that every city is connected to all the other 3 cities.
If we start from city A, there are 3 ways in which we can proceed, viz. AB, AD or AC.
Once we are at any of these cities, each one of them is connected to the other 3 cities. But since we cannot go back to city A, there are only 2 ways in which we can proceed from here.
If we are at B, we can take either paths BD or BC.
From this point, we have a choice of going directly to A (thus skipping 4th city) or go to 4th city and come back to A. Eg. If we are at D, we can either take DA or DCA. So there are 2 more ways to go from here.
Hence, required number of ways = 3 × 2 × 2 = 12.
Hence, option (b).
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