Question

There are 23 buses available between Dinu's house and his school. How many ways are possible for Dinu to go from his house to school and return using different buses?

• A. 529
• B. 506
• C. 463
• D. 484

Hint:

Always subtract the "already used" option from the total if the question specifies that items or routes cannot be repeated (different buses, no repetition, etc.).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This involves two sequential events where the second event is dependent on the choice of the first event because a "different" bus must be used for the return journey.

Step 2: Key Formula or Approach:
Total ways = (Ways to go) $\times$ (Ways to return)

Step 3: Detailed Explanation:
1. Going to school: There are 23 buses available. So, Dinu has 23 ways to go to school. 2. Returning home: He must use a different bus than the one he took to school. 3. Therefore, available buses for return = $23 - 1 = 22$ buses. 4. Total ways = $23 \times 22$. \[ 23 \times 22 = 23 \times (20 + 2) = 460 + 46 = 506. \]

Step 4: Final Answer:
There are 506 possible ways for Dinu to complete his journey.