Question:
A person travels from Hyderabad to Goa and returns, but does not use the same bus for both journeys. If there are 25 buses available for each direction, how many ways can the round trip be made?
A person travels from Hyderabad to Goa and returns, but does not use the same bus for both journeys. If there are 25 buses available for each direction, how many ways can the round trip be made?
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In "round trip without repetition" problems, if there are $n$ options, the answer is always $n(n-1)$. If the same bus could be used, it would be $n^2$.
Updated On: Apr 16, 2026
- 600
- 625
- 650
- 700
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept
This is a problem based on the Fundamental Principle of Counting (Multiplication Rule). We need to choose one bus for the forward journey and one for the return journey under a specific constraint.
Step 2: Detailed Explanation
1. Forward Journey (Hyderabad to Goa): There are 25 buses available. Number of ways = 25. 2. Return Journey (Goa to Hyderabad): The person cannot use the same bus used in the forward journey. Number of available choices = $25 - 1 = 24$. 3. Total Ways: \[ \text{Total ways} = 25 \times 24 = 600 \]
Step 3: Final Answer
The round trip can be made in 600 ways.
This is a problem based on the Fundamental Principle of Counting (Multiplication Rule). We need to choose one bus for the forward journey and one for the return journey under a specific constraint.
Step 2: Detailed Explanation
1. Forward Journey (Hyderabad to Goa): There are 25 buses available. Number of ways = 25. 2. Return Journey (Goa to Hyderabad): The person cannot use the same bus used in the forward journey. Number of available choices = $25 - 1 = 24$. 3. Total Ways: \[ \text{Total ways} = 25 \times 24 = 600 \]
Step 3: Final Answer
The round trip can be made in 600 ways.
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