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?
The correct answer is (C) 15.
Explanation:
A person can travel from A to C through two main mutually exclusive paths: directly from A to C, or via B. There are 3 different direct roads from A to C. For traveling via B, there are 3 different roads from A to B and 4 different roads from B to C, giving 3 × 4 = 12 different ways to travel from A to C via B using the fundamental counting principle. Adding both paths, the total number of different ways is 3 + 12 = 13 ways. Hence, option (b) is correct.
हिंदी में प्रश्न एवं आदर्श उत्तर
A, B और C तीन स्थान इस प्रकार हैं कि A से B के लिए तीन भिन्न रास्ते हैं, B से C के लिए चार भिन्न रास्ते हैं और A से C के लिए तीन भिन्न रास्ते हैं। इन रास्तों का प्रयोग कर कोई व्यक्ति कितने भिन्न मार्गों से A से C तक जा सकता है?
सही उत्तर (C) 15 है।
व्याख्या:
A person can travel from A to C through two main mutually exclusive paths: directly from A to C, or via B. There are 3 different direct roads from A to C. For traveling via B, there are 3 different roads from A to B and 4 different roads from B to C, giving 3 × 4 = 12 different ways to travel from A to C via B using the fundamental counting principle. Adding both paths, the total number of different ways is 3 + 12 = 13 ways. Hence, option (b) is correct.