if there are 3 roads from Town A to Town B and 4 roads from Town B to Town C. How many ways can one go from Town A to C and back to Town A through the Town B without passing through the same road twice?
This problem can be solved using the Fundamental Principle of Counting or FPC. The FPC states that if one event can be done in [tex]m[/tex] ways and another event can be done in [tex]n[/tex] ways, the number of ways that the two events can happen is [tex]mn[/tex] ways. For example, if you have 2 different shirts and 5 different pair of pants, the number of possible combinations of a shirt and a pair pants that you can make is 2×5 = 10 ways.
Now, to solve this problem, we have to remember that the route is this: From A to B, then from B to C, then from C back to B, and from B back to A.
Let’s count our choices:
(a) From A to B, we have 3 roads to choose from;
(b) From B to C, we have 4 roads to choose from;
(c) In going back from C to B, we only have 3 options this time since we already took one in (b), again we cannot take the same road twice;
(d) From B to A, we only have 2 roads to choose from since we already took one in (a).
Therefore, applying the FPC now, we have a total of 3×4×3×2 = 72 ways.
See another problem that uses FPC: brainly.ph/question/279814
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