A, B and C are three places such that there are three different roads from A to B, four different roads from B to C and three different roads from A to C. In how many different ways can one travel from A to C using these roads?
- A10
- B13
- C15Correct
- D36
Explanation
The problem asks for the total number of different ways to travel from A to C. There are two distinct scenarios to consider:
-
Traveling directly from A to C: There are 3 different roads given from A to C.
-
Traveling from A to C via B: First, one must travel from A to B. There are 3 different roads from A to B. Then, one must travel from B to C. There are 4 different roads from B to C. To find the total number of ways to travel from A to B and then to C, we multiply the number of ways for each segment (Multiplication Principle). Number of ways via B = (Roads A to B) * (Roads B to C) = 3 * 4 = 12 ways.
Since these two scenarios (direct travel and travel via B) are mutually exclusive ways to reach C from A, we add the number of ways from each scenario to find the total number of ways (Addition Principle).
Total ways = (Ways directly A to C) + (Ways via B) Total ways = 3 + 12 = 15 ways.
Therefore, one can travel from A to C in 15 different ways.
The final answer is C.
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