Question

There are $ 5 $ roads leading to a town from a village. The number of different ways in which a villager can go to the town and return back is,
A. $ 25 $
B. $ 20 $
C. $ 10 $
D. $ 5 $

Answer 1

Hint: Use the number of ways given to move from village to town and the number of ways to return back and then find the total number of ways for moving to town from village and returning back by using the multiplication principle.

Complete step-by-step answer:
It is given in the question that there are only $ 5 $ roads leading to a town from the village.
So, the number of ways to move from village to town is equal to $ 5 $ as they can travel from any of the roads.
Now to move back from town to village the villager is left with only $ 4 $ roads out of the total roads.
So, the number of ways to move from town to village is equal to $ 4 $ .
So, the total number of ways for the total journey is equal to $ 5 \times 4 = 20 $ ways.
So, the number of different ways in which a villager can go to the town and return back is equal to $ 20 $ .
So, the correct answer is “Option B”.

Note: The multiplication principle says that the number of ways for occurring of one event is equal to $ m $ and the number of ways for occurring of another event is equal to $ n $ then the number of ways of occurring both the events together is equal to $ mn $ .