Question

There are 4 roads between towns A and B, and 3 roads between towns B and C. How many different ways can a person travel from A to C via B and return to A without using the same road more than once in each direction?

• A. 144
• B. 12
• C. 72
• D. 24

Hint:

When no repetition is allowed, subtract one choice from each reverse direction. Multiply total forward and reverse combinations.

Answer 1

The Correct Option is C

From A to B: 4 options From B to C: 3 options Total ways A → B → C = \( 4 \times 3 = 12 \) Return trip:
C → B (don’t use same road as B → C): 2 options
B → A (don’t use same as A → B): 3 options
Return trip = \( 2 \times 3 = 6 \) So total distinct round-trips = \( 12 \times 6 = \boxed{72} \)